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ARITHMETICAL  PROBLEMS, 


AREANGED  FOE 


DRILL    AND    REVIEW 


IN 


PRIMARY,  GRAMMAR,  AND  HIGH  SCHOOLS. 


By  E.  WENTWORTH, 

PRINCIPAL   OF    NORTH    SCHOOL,    PORTLAND,    ME. 

JOHN  S.  PRELL 

Qvil  &  Mechanical  Engineer. 

SAJtf  FBANCISCO,  CAL. 


NEW  YOKE : 
HARPER    &    BROTHERS, 

FRANKLIN   SQUARE. 

1884. 


VBC47I0S  LIMU 


Entered  according  to  Act  of  Congress,  in  the  year  1872,  by 

II  A  R  PER    &    BROTHERS, 
in  ihc  Office  of  the  Librarian  of  Congress,  at  Washington. 


Is'i^tJtMlO^ 


Add  to  Lib, 
GIFT 


PREFACE. 


HAVING  felt  the  necessity  of  a  larger  number  of  pro- 
gressive examples  for  practice  than  is  usually  found  in 
the  text-books,  in  order  to  secure  accuracy  and  rapidity  in 
arithmetical  operations,  I  prepared,  some  time  since,  and  used 
in  my  own  school,  most  of  the  examples  included  in  the  first 
three  chapters  of  this  book ;  and  by  request  of  many  expe- 
rienced teachers,  additions  have  been  made  to  those  examples, 
and  the  work  is  now  offered  to  the  public ;  not,  however,  as  a 
rival  to  any  other  text-book,  but  as  one  designed  to  be  used 
with,  and  supplementary  to,  any  text-book  in  use. 

Experience  shows  that  much  time  is  lost  by  inaccuracy  in 
computation,  and  that  many  pupils  who  can  perform,  satisfac- 
torily, examples  arranged  under  certain  rules,  fail  to  perform 
original  and  miscellaneous  examples,  given  by  the  teacher, 
even  though  more  simple  and  involving  the  same  processes ; 
because  before  one  principle  with  its  applications  is  under- 
stood, another  is  thrust  upon  them. 

I  have  endeavored  to  obviate  these  difficulties  by  arranging 
the  work  in  such  order  as  to  test  the  ability  of  the  pupils  upon 
any  given  topic,  and  to  furnish  a  thorough  drill.  Therefore 
the  distinguishing  feature  of  this  work  is,  that  each  subject  is 
first  treated  separately,  with  at  least  twenty-five  examples, 
without  answers,  rules,  tables,  or  suggestions ;  including  every 
form  of  rules  pertaining  to  the  subject,  so  that  in  a  class  of 
from  twenty-five  to  thirty,  each  pupil  can  have  a  different 
example;  then  a  large  number  and  variety  of  Promiscuous 

923 


IV  PKEFACE. 

Examples  are  given,  involving  all  the  preceding  rules,  and  so 
arranged  as  to  require  a  practical  knowledge  of  them.  The 
book  is  divided  into  four  chapters. 

The  First  Chapter  is  confined  to  operations  in  the  Funda- 
mental Kules,  United  States  Money,  and  Compound  Num- 
bers ;  and  is  designed  for  Primary  and  the  lower  grades  of 
Grammar  Schools. 

The  Second  Chapter  includes  Common  and  Decimal  Frac- 
tions ;  and  the  Third,  Percentage,  with  its  applications,  Part- 
nership, Proportion,  Square  and  Cube  Boots ;  and  is  designed 
for  Grammar  Schools. 

The  Fourth  Chapter  embraces  the  whole  subject  of  Arith- 
metic, and  is  designed  for  High  School  work.  This  Chapter 
was  prepared  by  Mr.  A.  P.  Stoke,  Principal  of  the  Portland 
High  School,  to  whom  I  am  under  special  obligations  for 
valuable  suggestions,  as  well  as  the  preparation  of  this  Chap- 
ter. 

E.  WENTWOKTH. 

Portland,  April,  1812, 


CHAPTER   U 

PRILL    AND    REVIEW    EXERCISES    IN    THE    ELEMENTARY 

RULES  OF  ARITHMETIC,  UNITED  STATES  CURRENCY 

AND  COMPOUND  NUMBERS. 

Write  the  following  numbers : 

1.  Forty  million,  fifteen  thousand,  seven  hundred. 

2.  Six  hundred  three  million,  four  thousand,  seventy-five. 

3.  Twelve  billion,  thirty  million,  one  thousand,  two  hundred. 

4.  Five  hundred  thousand,  eight  hundred  forty-seven. 

5.  One  hundred  million,  seven  thousand,  four  hundred. 

6.  Seven  hundred  fifty  billion,  sixty  thousand,  thirty-four. 

7.  Three  million,  four  hundred  nine  thousand,  twelve. 

8.  Two  hundred  billion,  thirteen  million,  seven  thousand. 

9.  Four  hundred  five  million,  three  hundred  fifty  thousand. 

10.  One  hundred  sixty  thousand,  five  hundred  nineteen. 

11.  Seven  hundred  ten  million,  seven  thousand,  ten. 

12.  Eighteen  billion,  fifty  thousand,  four  hundred  one. 
IS.  Two  hundred  million,  ten  thousand,  nine  hundred. 
lJf.  Ten  billion,  forty  million,  three  hundred  twelve. 

15.  One  hundred  one  million,  ten  thousand,  one  hundred. 

16.  Ninety  million,  five  hundred  thousand,  twenty-three. 

17.  Ten  million,  twenty-seven  thousand,  nine  hundred  ten. 

18.  Twelve  million,  one  thousand,  eight  hundred  forty. 

19.  One  hundred  sixty  million,  one  hundred  thousand. 

20.  Forty-seven  thousand,  two  hundred  eleven. 

21.  Eleven  billion,  four  million,  four  hundred  thousand. 

22.  Three  hundred  fifty  million,  eleven  thousand,  forty. 

23.  Twenty-six  billion,  seventy-five  thousand,  one  hundred. 

24.  Four  hundred  million,  ten  thousand,  five  hundred  thirty. 

25.  Seventeen  billion,  eight  million,  three  hundred  five. 

26.  Five  billion,  ninety  thousand,  one  hundred  eleven. 


ARITHMETICAL  EXAMPLES. 


[CHAP.   I. 


27. 

28. 

29. 

SO. 

91 

5240172 

470249 

39862 

9142634 

538142 

367046 

9080560 

463059 

573127 

21-960 

54170 

25453 

72403 

2401840 

8243576 

7023942 

207J35 

6512920 

75064 

734205 

629405 

3401067  . 

4147 

3120300 

4095478 

40372 

4721 

8094625 

625810 

162U50 

82. 

83. 

84. 

35. 

36. 

28054 

1207642 

9067890 

5756427 

4763256 

12345 

56574 

7543267 

244604 

987635 

579635 

7966 

612343 

1135072 

903 

97054 

4346025 

5075172 

623429 

5635140 

761456 

152409 

412746 

9421560 

263104 

16044 

047531 

2104355 

4036357 

7256422 

\         87. 

38. 

39. 

& 

it 

532769 

768910G 

545684 

4962347 

372421 

4305175, 

227531 

2307528 

230524 

59055 

8143324 

980406 

260135 

3075125 

4920 

3607 

3409082 

9072410 

406862 

42364 

57843 

65743 

307086 

7210490 

541647 

5420653 

6445077 

4240734 

642067 

8205402 

Jf, 

43. 

4Jh   >~^ 

45. 

46. 

365463 

5234709 

981742 

863247 

199380 

4641901 

52470 

2470545 

3277801 

7434275 

356264 

6090514 

9402074 

9028056 

821068 

741045.7 

720086 

59217 

139208 

5932407 

99108' 

$405365 

870648 

2475416 

852064 

9102596 

74207 

5243466 

958745 

433226 

47.  ~* 

48. 

49. 

50. 

51. 

6375732 

2464725 

785634 

2069743 

15049:2 

509428 

3982414 

7856340 

9507651 

7401 6S0 

1927109 

573528 

125401 

650264 

43172, 

9056290 

491736. 

954178 

7510395 

573273 

473506 

4182647 

4035274 

422581 

9190285 

85145 

8053^25 

5603480 

634076 

475047 

CHAP.   I.] 


ARITHMETICAL  EXAMPLES. 


52. 
8147265215 
2538627431 

53. 
705421946 
5186049 

5 
40057100425 
5184241162 

55. 
5204140053 
295224327 

56. 
231462324 
194040575 

57. 
10435127315 
6380743646 

58. 
9360402180 
6875028407 

59. 
521460132 
250382409 

60. 
15000314031 
2138405118 

61. 
2244270120 
807422053 

62. 
850075426 
509480098 

63. 

95100365400 

9247087502 

64. 

4000000000 
2105250047 

65. 

342164312 

87328170 

66. 
87043143235 
194528369 

67. 
6112431263 
5370643198 

68. 
415316400 

327807749 

69. 
75120351312 
65487274504 

70. 
7501324132 
924165324 

71. 
621123231 
130591655 

72. 
33530245110 
23915637528 

73. 
5210425231 
3842178324 

7* 

710942162 
92687085 

77. 
127310213 

78506405 

75. 
64500002190 
927436244 

76. 
1002010101 
409607512 

78. 
99234040512 
5471362476 

79. 
3123400123 
634569342 

80. 
500500500 
37537137 

81. 
11215131200 
4427365485 

8  ARITHMETICAL    EXAMPLES.  [CHAP.   I. 

82.  Add  five  hundred  five  thousand,  five  hundred  five; 
twenty-four  thousand  forty ;  thirty  thousand  three  hundred ; 
thirty-one  thousand  fifty. 

83.  Subtract  seven  million,  fifty-seven  thousand,  nine  hun- 
dred twenty-nine,  from  three  hundred  forty-six  million,  one 
hundred  one  thousand. 

8Jh  Add  eighty-seven  thousand,  two  hundred  one ;  two  hun- 
dred fifty  thousand  eight  hundred ;  eight  hundred  thousand 
eighty-seven ;  four  hundred  forty-nine. 

85.  From  forty-seven  million,  three  hundred  one  thousand 
thirty,  take  four  hundred  eighty-three  thousand,  three  hun- 
dred thirteen.  . 

86.  Add  fifty  million  fifty ;  ten  thousand  ten ;  one  million, 
twenty  thousand  eight  hundred ;  thirty  thousand  six  hundred. 

87.  From  ninety  million,  thirty  thousand  thirty,  take  seven 
million,  six  hundred  forty  thousand,  five  hundred  seventy* 
eight. 

88.  What  is  the  sum  of  five  billion,  twenty  million,  one  thou- 
sand eight ;  one  hundred  fifty  million  sixty  thousand ;  three 
hundred  four  million,  ten  thousand,  two  hundred  fifty-eight  ? 

89.  From  one  hundred  five  billion  take  twelve  million,  sixty- 
four  thousand  twenty-five. 

90.  Find  the  amount  of  seven  hundred  million,  two  hundred 
sixteen  thousand  two  hundred;  forty  million,  nine  hundred 
seventy-five ;  eight  thousand  fourteen. 

91.  Subtract  eight  hundred  seventy  thousand,  three  hun- 
dred fifty,  from  twenty-seven  million,  nine  thousand  eighteen. 

92.  Add  ten  million,  thirty  thousand,  six  hundred  eight ; 
ninety  thousand,  five  hundred  seventeen ;  four  million  three 
hundred  sixty-five  thousand ;  one  million  seven  hundred  sixty. 

93.  From  one  hundred  twenty-seven  million,  five  thousand 
five,  take  ninety  million,  twelve  thousand  eighty-seven. 

9Jf.  What  is  the  sum  of  two  million  four  hundred  twelve 
thousand;  twenty-four  million,  live  thousand  twenty;  six 
hundred  thousand  forty-four;  forty  million,  three  hundred 
seventy-five  ? 


CHAP.  I.]  ARITHMETICAL  EXAMPLES.  9 

95.  From  eight  hundred  thousand  take  ninety  thousand, 
nine  hundred  sixty-nine. 

96.  Add  seven  hundred  thousand,  two  hundred  sixty ;  twelve 
million  twelve;  fifty  thousand  four  hundred;  six  million, 
two  thousand  twenty  seven. 

97.  From  three  million,  sixty-five  thousand  three,  take  six 
hundred  thirty-eight  thousand,  four  hundred  nineteen. 

98.  Add  twenty  thousand,  five  hundred  eleven ;  four  mil- 
lion, seven  hundred  thousand  thirty ;  two  thousand  ninety ; 
four  hundred  thousand,  seven  hundred  four. 

99.  Subtract  seventy-five  million,  eighty-eight  thousand, 
seven  hundred  fifty-four,  from  five  hundred  million. 

100.  Add  nineteen  billion  sixteen ;  thirty  million,  six  hun- 
dred forty-seven  thousand  sixty-three ;  eight  million,  twenty 
thousand,  two  hundred  forty-nine. 

101.  From  four  hundred  twenty  billion,  five  thousand  seven, 
take  three  hundred  forty  billion,  thirty  thousand  four. 

102.  Add  eighty-four  million  fifteen ;  sixty-seven  thousand 
sixty-eight ;  five  million,  ten  thousand  seventeen ;  three  hun- 
dred thousand  twenty ;  three  million,  eight  thousand  seventy- 
five.  — 

103.  From  one  million,  six  thousand  nine,  take  seventy 
thousand,  five  hundred  eight. 

lOlf.  What  is  the  sum  of  two  million,  seven  thousand  eigh- 
teen; three  hundred  five  thousand  nineteen;  nineteen  mil- 
lion, five  hundred  thousand;  two  million,  four  hundred 
twenty  ? 

105.  Subtract  four  hundred  twenty-five  million,  thirty- 
seven  thousand,  nine  hundred  fifty-three  from  one  billion. 

106.  Find  the  sum  of  twelve  billion,  thirteen  million,  forty 
thousand ;  twenty  million,  three  hundred  thousand,  six  hun- 
dred; one  hundred  thirty  thousand  thirty;  seven  thousand, 
two  hundred  five. 

107.  Subtract  nine  hundred  thousand,  four  hundred  fifty- 
seven  from  ten  million,  one  hundred  five  thousand,  two  hun- 
dred eleven. 


10 


ARITHMETICAL   EXAMPLES. 


[CHAP.    I. 


108. 

109. 
110. 
111. 
112. 
113. 
114. 
115. 
116. 
117. 
118. 
119. 
120. 
121. 


123. 
124. 
125. 
126. 
127. 
128. 
129. 
130. 
131. 
132. 
183. 
184. 
135. 
136. 
137. 
138. 
139. 
140. 
141. 
142. 
143. 

144. 
145. 


Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 
Multiply 


5469326  by  4 
4625075  by  7 
3250467  by  3 
9873672  by  5 
6708423  by  2 
7530647  by  8 
5069384  by  4 
6304867  by  6 
5940685  by  7 
3094723  by  5 
8549308  by  9 
409857  by  3 ; 
690574  by  6 ; 
5704685  by  8 
968037  by  4 ; 
6290874  by  7 
375486  by  6 ; 
3286754  by  3 
7209948  by  5 
2587049  by  7 
864754  by  4 ; 
247825  by  6 ; 
508637  by  2 ; 
7542964  by  9 
8057492  by  4 
5460748  by  7 
9208476  by  2 
5703928  by  8 
7435039  by  5 
4827046  by  7 
3590867  by  4 
4068137  by  6 
3562853  by  5 
4209473  by  7 
9574087  by  4 
8362409  by  3 
7290438  by  5 
3782905  by  6 


by  35  ;  by  627. 

by  46;  by  432^ 

by  24;  by  576. 

by  62;  by  348. 

by  53;  by  467. 

by  46;  by  357. 

by  72;  by  563. 

by  49;  by  826. 

by  38;  by  605. 

by  45;  by  921. 

by  82;  by  476. 
by  48;  by  295. 
by  37:  by  548. 
;  by  52;  by  290. 
by  28.;  by  407. 

by  48;  by  825. 
by  74 ;  by  647. 

by  57;  by  365. 

by  38;  by  643. 

by  29;  by  286. 
by  54;  by  519. 
by  54;  by  273. 
by  76;  by  543. 

by  47;  by  625. 

by  68 ;  by  357. 

by  38;  by  402. 

by  73;  by  456. 

by  92;  by  167. 

by  75;  by  462. 

by  42;  by  305. 

by  64;  by  537. 

by  72;  by  435. 

by  45;  by  382. 

by  83  ;  by  250. 

by  92;  by  538. 

by  57;  by  426. 

by  36;  by  407. 

by  74;  by  358. 


CHAP.    I.] 


AKITHMETICAL   EXAMPLES. 


11 


14-6. 
U7. 

148. 
149. 
150. 
151. 
152. 
153. 
15^. 
155. 
156. 
157. 
158. 
159. 
160. 
161. 
162. 
163. 
164. 
165. 
166. 
167. 
168. 
169. 
170. 
171. 
172. 
173. 

174. 
175. 
176. 
177. 
178. 
179. 
180. 
181. 
182. 
183. 


Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 
Divide 


4705342  by  2 ; 
5063728  by  5 ; 
2531049  by  7 ; 
6108590  by  4 ; 
1372427  by  3 ; 
9420305  by  6 ; 
6027148  by  9 ; 
7425915  by  8 ; 
3704520  by  5 ; 
4132576  by  2 ; 
29504314  by  4 
34567891  by  6 
2573468  by  8 
2791548  by  7 
7294682  by  5 
7805345  by  9 
3720423  by  3 
5378042  by  6 
4708197  by  4 
5043706  by  2 
6570523  by  6 
4976854  by  9 
5092756  by  3 
7806972  by  6 
2483057  by  8 
2950726  by  5 
7043295  by  2 
980G257  by  4 
2354075  by  7 
5043746  by  5 
8542308  by  9 
4912734  by  4 
6304567  by  8 
1246859  by  2 
8642357  by  7 
90470653  by  4 
52740846  by  6 
38504275  by  3 


by  63; 
by  72; 
by  81; 
by  92; 
by  56; 
by  47; 
by  38; 
by  45; 
by  64; 
by  37; 
:  by  53 
;  by  65 
by  73 
by  85 
by  42 
by  36 
by  74 
by  57 
by  63 
by  94 
by  75 
by  26 
by  57 
by  43 
by  27 
by  48 
by  93 
by  53 
by  19 
by  64 
by  17 
by  57 
by  42 
by  84 
by  36 
;  by  18 
;  by  45 
;  by  72 


by  455. 

by  346. 

by  532. 

by  138. 

by  472. 

by  352. 

by  274. 

by  732. 

by  273. 

by  465. 
;  by  621. 
;  by  149. 

by  426. 

by  243. 

by  673. 

by  547. 

by  629. 

by  348. 

by  529. 

by  357. 

by  418. 

by  350. 

by  146. 

by  572. 

by  345. 

by  162. 

by  435. 

by  171. 

by  439. 

by  723. 

by  456. 

by  167. 

by  536. 

by  719. 

by  453. 
;  by  160. 
;  by  914. 
;  by  465. 


12  ARITHMETICAL   EXAMPLES.  [CHAP.  L 

18^.  If  the  multiplicand  is  9476  and  the  multiplier  367, 
what  is  the  product  ? 

185.  If  76  hogsheads  of  molasses  cost  2888  dollars,  what  is 
the  price  of  1  hogshead  ? 

186.  Sold  29  bales  of  cloth,  each  containing  35  yards,  at 
75  cents  per  yard ;  how  much  did  I  receive  ? 

187.  What  cost  749  gallons  of  vinegar  at  28  cents  per  gallon  ? 

188.  Divide  one  hundred  eighty-four  thousand,  seven  hun- 
dred seventy-five  dollars  among  389  men  ? 

189.  If  one  acre  of  land  costs  45  dollars,  what  will  4721 
acres  cost  ? 

190.  Multiply  forty-nine  thousand  seventy-eight  by  four 
hundred  eight  ? 

191.  Bought  75  bushels  of  corn  at  92  cents  per  bushel,  and 
87  bushels  of  oats  at  65  cents  per  bushel;  what  was  the 
amount  of  the  corn  and  oats  ? 

192.  If  237  bags  of  coffee  cost  20145  dollars,  what  cost  ono 
bag? 

193.  What  is  the  difference  between  one  million,  and  nine 
thousand  seventy-four  ? 

IDlf..  What  cost  125  horses  at  250  dollars  apiece,  and  235 
cows  at  65  dollars  apiece  ? 

195.  What  is  the  weight  of  755  barrels  of  flour,  each  weigh- 
ing 196  pounds  ? 

196.  A  man  owing  9475  dollars  gives  in  payment  45  acres 
of  land  valued  at  37  dollars  per  acre  and  $5000  in  cash ;  how- 
much  remains  unpaid  ? 

197.  How  many  bales  will  1072512  pounds  of  cotton  make, 
allowing  294  pounds  to  the  bale  ? 

198.  A  farmer  sold  1125  bushels  of  wheat  for  96  cents  a 
bushel,  942  bushels  of  oats  for  43  cents  a  bushel,  ami 
bushels  of  corn  for  75  cents  a  bushel.    How  much  did  he 
receive  ? 

199.  A  trader  bought  975  bushels  of  wheat  for  95  cents  a 
bushel  and  sold  it  for  99  cents  a  bushel ;  how  much  did  he  gain  ? 

200.  How  many  times  is  216  contained  in  1554768  ? 


CHAP.  I.]  AEITHMETICAL  EXAMPLES.  13 

201.  Bought  85  barrels  of  apples  at  4  dollars  a  barrel,  36 
barrels  of  potatoes  at  2  dollars  a  barrel,  and  25  tons  of  hay  at 
27  dollars  per  ton,  and  sold  the  same  for  1500  dollars;  how 
much  was  gained  ? 

202.  At  25  dollars  per  acre,  how  much  will  840  acres  of 
land  cost  ? 

203.  If  a  man  travel  34  miles  a  day,  how  long  will  it  take 
him  to  travel  2210  miles  ? 

20£.  If  a  field  of  640  acres  produces  14720  bushels  of  wheat, 
how  much  will  1  acre  produce  ? 

205.  A  merchant  bought  25  hogsheads  of  molasses  at  40 
dollars  each,  and  paid  750  dollars  down ;  how  much  remained 
unpaid  ? 

206.  A  merchant  sold  26  pieces  of  cloth,  each  piece  con- 
taining 42  yards ;  how  many  yards  were  there  ? 

207.  In  how  many  days  will  a  ship  sail  5075  miles,  if  it 
sails  140  miles  each  day  ? 

208.  What  must  be  paid  for  742  bushels  of  wheat  at  2  dol- 
lars per  bushel,  86  barrels  of  flour  at  9  dollars  per  barrel,  and 
229  barrels  of  pork  at  19  dollars  per  barrel  ? 

209.  Sold  892  tons  of  hay  at  28  dollars  per  ton ;  how  much 
did  I  receive  ? 

210.  A  speculator  bought  land  for  218568  dollars  at  42  dol- 
lars per  acre ;  how  many  acres  did  he  purchase  ? 

211.  Bought  95  hogsheads  of  molasses  at  56  dollars  per 
hogshead,  and  sold  it  at  75  dollars  per  hogshead ;  what  was 
gained  ? 

212.  Sold  148  cords  of  wood  at  8  dollars  per  cord,  57  tons 
of  timber  at  24  dollars  per  ton,  and  45  cords  of  bark  at  12 
dollars  per  cord ;  what  was  the  amount  received  ? 

213.  At  29  dollars  per  barrel,  how  many  barrels  of  sugar 
can  be  bought  for  30305  dollars  ? 

211f.  If  a  person  travel  -45  miles  a  day,  how  far  will  he  travel 
in  96  days  ? 

215.  If  1578  barrels  of  beef  ure  sold  for  23670  dollars,  what 
is  the  price  of  one  barrel  ? 


14  ARITHMETICAL    EXAMPLES.  [CHAP.   I. 

216.  Add  27  x  39  and  1969  x  4. 

217.  298  x  10  minus  25  x  37  =  what  ? 

218.  Multiply  242  —  127  by  140  +  133  +  27. 

219.  2103  +  1G14  multiplied  by  83  —  75  =  what? 

220.  Add  114  x  40  and  370  x  63. 

221.  2044  x  32  divided  by  55  —  41  =  what? 

222.  Subtract  4248  -r-  8  from  787  x  5. 

223.  155  x  400  plus  1350  +  2530  +  2820  =  what? 

224.  Multiply  572  +  267  +  128  by  112  —  62. 

225.  Add  86  x  64  and  1081  x  32. 

226.  422  x  16  minus  313  x  4  =  what? 

227.  Divide  252  x  50  by  27  -r-  9. 

228.  Add  162  x  126  and  8  x  5377. 

229.  951  —  627  multiplied  by  1000  -v-  40  =  what? 

230.  Subtract  961  +  782  +  116  from  4087. 

231.  817  X  12  plus  5193  -r-  3  =  what  ? 

232.  Divide  147  x  40  by  600  —  110. 

233.  What  is  the  difference  between  175  x  10  and  8750-r-lO? 

234.  Add  4400  +  1281  +  3790  and  471  -f- 157. 

235.  Multiply  30060  +  28765  by  12  —  4. 

236.  What  is  the  difference  between  1182  x  7  and  1463  x  4? 

237.  31920  -f-  2660  multiplied  by  173  x  8  =  what  ? 

288.  163  x  23  plus  441  x  20  =  what  ? 

289.  660  -f-  3  minus  2106  -r-  162  =  what  ? 

240.  Divide  4311  x  32  by  3  +  8  +  1. 

241.  330  —  214  multiplied  by  528  —  128  =  what  ? 
829  +  516  +  724  minus  480  +  560  +  380  =  what  ? 
Add  1666  -  1254  and  7650  -f-  9. 

244.  What  is  the  difference  between  8303  and  1284—1171  ? 
Divide  68040  -r-  7  by  45  -r-  3. 
218  —  182  multiplied  by  110  —  94  =  what  ? 

247.  28015  +  22205  divided  by  25  +  42  +  14  =  what? 

248.  1500  —  482  plus  436  +  225  =  what  ? 

249.  Add  82  +  118  and  418  —  118. 

250.  Multiply  100  x  10  by  500  ^  100. 

251.  What  is  the  difference  between  800  x  5  and  12500-^-5  ? 

252.  4433  x  4  divided  by  10  .+  11  +  10  =  what? 
258.  Subtract  5979  —  167  from  7830  +  167. 


CHAP.  I.]  ARITHMETICAL  EXAMPLES.  15 

Write  the  following  numbers : 

251f.  Five  hundred  dollars,  five  cents,  four  mills. 

255.  Four  hundred  eagles,  eight  dollars,  three  dimes,  two  cts. 

256.  Three  hundred  ten  dollars,  one  cent,  two  mills. 

257.  Two  million  thirty  thousand  dollars,  thirty-seven  cents. 

258.  Fifty  million  dollars,  twelve  and  one-half  cents. 

259.  Seventy -five  thousand  fifteen  dollars,  seven  mills. 

260.  Five  and  one-half  eagles,  five  and  one-half  dimes. 

261.  Seven  hundred  twenty-five  dollars,  two  cents  nine  mills. 

262.  Six  hundred  two  dollars,  six  dimes,  eight  cts.,  three  mills. 

263.  Eight  hundred  sixty  dollars,  eighteen  cents,  four  mills. 
26Jf.  Fifty  dollars,  five  cents,  nine  mills. 

265.  Twenty  thousand  dollars,  seventeen  cents,  five  mills. 

266.  Three  eagles,  nine  dollars,  fifty  cents. 

267.  One  hundred  eagles,  seventy-five  cents,  eight  mills. 

268.  Fifty  thousand  dollars,  thirty-seven  cents. 

269.  Nine  hundred  one  dollars,  ninety  cents. 

270.  One  thousand  ten  dollars,  one  cent,  one  mill. 

271.  One  hundred  dollars,  ten  cents,  one  mill. 

272.  One  hundred  thousand  ten  dollars,  nine  cents. 

273.  Seventy-five  dollars,  ten  cents,  two  mills. 

271f.  One  hundred  twenty  dollars,  two  cents,  five  mills. 

275.  Five  thousand  forty  dollars,  fifteen  cents. 

276.  Seven  hundred  ten  dollars,  four  cents,  six  mills. 

277.  Twenty  thousand  dollars,  seventy-five  cents. 

278.  Thirty-five  thousand  one  dollars,  twelve  cents. 

279.  One  thousand  fifty  dollars,  fifty  cents. 

280.  Ten  dollars,  one  cent,  one  mill. 

281.  Ninety-nine  dollars,  nine  dimes,  three  cents. 

282.  One  hundred  dollars,  ten  cents,  nine  mills. 

283.  Forty  eagles,  seven  dollars,  two  dimes,  eight  mills, 

284.  Twenty  thousand  twenty  dollars,  five  cents. 

285.  Four  thousand  nine  dollars,  seven  cents. 

286.  One  hundred  thousand  six  dollars,  thirty  cents. 

287.  One  dollar,  one  cent,  one  mill. 

288.  One  thousand  dollars,  ten  cents,  nine  mills. 

289.  Four  hundred  thousand  dollars,  eleven  cents. 

290.  Fifty  thousand  fifty  dollars,  fifty  cents. 


10  ARITHMETICAL  EXAMPLES.  [CHAP.  L 

291.  Reduce  7564  cents  to  dollars. 

292.  How  many  cents  in  $59806  ? 
298.  Change  569482  mills  to  dollars. 

294.  How  many  mills  in  $43.12  ? 

295.  Reduce  427  mills  to  cents. 

296.  How  many  cents  in  500  eagles  ? 

297.  Change  55  dollars,  six  cents,  five  mills  to  mills. 

298.  Reduce  75  dollars  to  cents. 

299.  How  many  dollars  in  57346  cents  ? 

800.  Reduce  450  mills  to  cents. 

801.  How  many  eagles  in  fifty  thousand  mills  ? 

802.  Reduce  eighty  thousand  cents  to  double  eagles. 
808.  Change  fifty-two  dollars  to  cents. 

801/..  How  many  cents  in  five  hundred  dollars  ten  cents  ? 

805.  Reduce  twenty-five  thousand  cents  to  dollars. 

806.  How  many  half  eagles  in  45000  cents  ? 

807.  Reduce  16525  mills  to  dollars. 

808.  In  7593  cents  how  many  dollars  ? 

809.  In  4369  mills  how  many  dollars  ? 

810.  Reduce  55050  mills  to  dollars. 

811.  In  12020  cents  how  many  dollars  ? 

812.  Reduce  59436  mills  to  cents. 

813.  In  one  thousand  dollars,  ten  cents,  nine  mills,  how 

many  mills  ? 

314.  Reduce  909  mills  to  cents. 

How  do  you  reduce  dollars  to  mills  ?    Why  ? 

315.  How  many  dimes  in  5  eagles  ? 

816.  How  many  mills  in  9  dimes  ? 

817.  Reduce  5  eagles,  5  dollars,  5  dimes  to  cents. 

818.  How  many  cents  in  50  eagles,  50  dollars,  50  dimes  ? 

819.  In  14750  cents,  how  many  dollars  ? 

How  do  you  reduce  dollars  to  cents  ?    Why  ? 

820.  In  11203  cents,  how  many  dollars  ? 

821.  Reduce  $15.25  to  cents. 

822.  How  many  cents  in  $100.01  ? 

828.  In  five  dollars,  two  cents,  how  many  mills  ? 

824.  In  5463  cents,  how  many  dollars  ? 

825.  How  many  dollars  in  15300  cents  ? 


CHAP.  I.]  AEITHMETICAL  EXAMPLES.  17 

326.  Add  fifteen  cents;  seven  hundred  fifty  dollars;  two 
dollars,  six  mills;  nine  mills;  twenty-five  dollars,  three  cents, 
and  one  mill. 

827.  Bought  a  barrel  of  flour  for  $9.50,  a  ton  of  coal  for 
$11.25,  a  barrel  of  sugar  for  $29.75,  and  a  box  of  raisins  for 
$3.75  J ;  what  was  paid  for  the  articles  ? 

828.  A  man  bought  a  horse  for  $180,  and  sold  him  for 
$220.50  ;  how  much  did  he  make  by  the  bargain  ? 

829.  What  will  4962  bushels  of  wheat  cost  at  one  dollar 
and  five  cents  a  bushel  ? 

330.  Paid  $848.02  for  389  barrels  of  apples;  what  was  the 
price  per  barrel  ? 

331.  At  $9.50  per  barrel,  how  many  barrels  of  flour  can  be 
bought  for  $2498.50  ? 

332.  A  man  bought  cows  at  $47.50  per  head ;  how  many 
could  he  buy  for  $3182.50  ? 

333.  Add  seventy- three  dollars,  eleven  cents ;  sixty-six  dol- 
lars, six  dimes ;  five  eagles,  five  cents ;  one  hundred  nine  dol- 
lars, nine  cents ;  and  six  hundred  dollars,  ten  cents,  five  mills. 

334..  If  200  pounds  of  pork  cost  $22,  what  is  the  price  per 
pound  ? 

335.  How  many  cords  of  wood,  at  $8.25  per  cord,  must  be 
given  for  900  pairs  of  shoes  at  $1.10  a  pair  ? 

336.  If  a  farm  of  84  acres  costs  $1233.96,  what  is  the  price 
of  one  acre  ? 

337.  Multiply  one  hundred  fifteen  dollars,  five  cents,  seven 
mills  by  four  hundred  eight. 

838.  From  $500  take  30  eagles,  six  dimes  and  six  mills. 

839.  If  ten  tons  of  coal  can  be  bought  for  $42.50,  what  is 
the  price  of  100  tons  at  the  same  rate  ? 

340.  What  is  the  price  of  5  bales  of  cotton,  each  weighing 
312  pounds,  at  $0,315  per  pound  ? 

341.  How  many  half  eagles  in  $4375  ? 

31$.  A  man  paid  $267  for  a  carriage,  and  157  dollars  12J 
cents  for  a  horse ;  how  much  more  did  he  pay  for  the  car- 
riage than  for  the  horse  ? 


18  AKITHMETICAL   EXAMPLES.  [CHAP.  L 

343.  Paid  175  dollars  and  eight  cents  for  a  carriage,  $200 
for  a  horse,  $145.75  for  a  yoke  of  oxen,  and  $12.15  for  a  plow ; 
how  much  was  paid  for  all  ? 

SJfJf.  At  $3.12  a  day,  how  much  will  a  man  earn  in  287  days  ? 

345.  What  cost  24  firkins  of  butter,  each  containing  47 
pounds,  at  38  cents  6  mills  per  pound  ? 

846.  A  drover  bought  743  cattle  for  $92875 ;  what  is  the 
average  price  of  each  ? 

34.7.  If  27  bags  of  coffee,  each  weighing  48  pounds,  cost 
$54432,  what  is  the  price  per  pound  ? 

848.  Eeduce  47968  mills  to  dollars. 

349.  If  75  reams  of  paper  cost  $243.75,  what  cost  157  reams  ? 

350.  A  lady  paid  $45.25  for  a  dress,  $15.62£  for  a  bonnet, 
$22.75  for  a  shawl,  and  gaye  in  payment  $100 ;  how  much 
ought  she  to  receive  ? 

351.  If  95  barrels  of  sugar  cost  $1095.35,  what  is  the  price 
of  a  barrel  ? 

352.  Bought  a  horse  for  $150,  a  wagon  for  $90.50,  a  harness 
for  twenty-three  dollars  six  cents,  and  a  buffalo  robe  for  $18| ; 
what  is  the  cost  of  all  ? 

853.  "What  cost  875  sheep  at  $5.12 £  per  head  ? 
854-  Paid  $268.40  for  610  boxes  of  strawberries ;  what  was 
the  price  per  box  ? 

855.  Sold  75  bushels  of  potatoes  at  56  cents  per  bushel, 
150  pounds  of  pork  at  16  cents  a  pound,  40  bushels  of  beans 
at  $2.25  per  bushel ;  how  much  was  received  for  all  ? 

How  do  you  reduce  dollars  to  cents  ?  to  mills  ?  mills  to 
dollars  ? 

856.  Add  $250.503 ;  7  eagles,  4  dimes,  6  mills;  12  dollars, 
15  cents ;  40  eagles,  20  cents ;  and  $400,  5  mills. 

857.  If  one  bushel  of  beans  costs  $2.3 7  J,  what  will  45  bush- 
els cost  at  the  same  rate  ? 

358.  How  many  quarter  eagles  in  $1857.50  ? 

859.  From  one  thousand  dollars  there  were  paid  to  one 
man  $57  eight  cents,  to  another  $175  three  cents,  to  another 
six  hundred  dollars ;  how  much  remained  ? 


CHAP.  I.]  ABITHMETICAL  EXAMPLES.  19 

360.  If  476  sheep  cost  $3213,  what  is  the  price  of  one  sheep  ? 

361.  If  I  purchase  a  horse  for  $125.37,  how  much  must  I 
pay  for  527  horses  at  the  same  rate  ? 

362.  At  $2.75  a  day,  how  much  will  a  man  earn  in  313  days  ? 

363.  Add  $5,125  +  $40.75  +  $13  and  five  mills  +  one  dol- 
lar, ten  cents. 

364.  If  395  acres  of  land  cost  $1860.45,  what  will  5  acres  cost  ? 

365.  A  lady  went  shopping  with  $10  in  her  purse ;  she  paid 
27  cents  for  needles,  $1.25  for  gloves,  and  three  dollars  for 
calico ;  how  much  had  she  left  ? 

366.  A  family  paid  for  flour  $23.15,  sugar  $5.62|,  butter 
$15.12J,  and  Deef  $20.25 ;  what  is  the  amount  ? 

867.  A  farmer  bought  a  yoke  of  oxen  for  $215  nine  cents,  a 
cow  for  $67.30,  sheep  for  $85  four  cents,  and  a  horse  for  $198 
five  cents ;  how  much  did  the  whole  cost  ? 

368.  What  will  8728  sheep  cost  at  $3.76  apiece  ? 

369.  Reduce  $20,275  to  mills. 

370.  If  254  cords  of  wood  cost  $2407.92,  what  is  the  price 
of  a  cord  ? 

371.  A  lady  bought  a  dress  for  $37.15,  a  bonnet  for  $12  six 
cents,  a  shawl  for  thirty  dollars  ten  cents,  and  a  pair  of  boots 
for  $3.62 ;  what  did  they  all  cost  ? 

372.  Bought  a  horse  for  $300  and  sold  him  for  $275  twelve 
cents ;  how  much  did  I  lose  ? 

373.  If  725  acres  of  land  cost  $18306.25,  what  was  the  cost 
of  one  acre  ? 

374.  From  one  hundred  dollars  take  nineteen  dollars  and 
seven  cents. 

375.  What  cost  527  bushels  of  wheat  at  $1.12^  a  bushel  ? 

376.  When  flour  is  $10.50  a  barrel,  how  many  barrels  can 
be  bought  for  $4462.50  ? 

877.  At  $12  and  five  mills  an  acre,  what  will  225  acres  of 
land  cost  ? 

378.  What  cost  6  doz.  Arithmetics  at  ninety-five  cts.  apiece  ? 
879.  If  25  Readers  cost  $22.17|,  what  is  the  price  of  each  ? 


20  ARITHMETICAL   EXAMPLES.  [CHAP.  1. 

880.  What  cost  13  barrels  of  sugar,  containing  224  pounds 
each,  at  12 \  cents  a  pound  ? 

381.  How  many  cords  of  bark  at  $5 \  a  cord,  will  pay  for 
fifty  barrels  of  sugar  at  $44  a  barrel  ? 

882.  If  220  bushels  of  corn  cost  $176,  what  is  the  price  per 
bushel  ? 

383.  How  many  bushels  of  wheat,  at  $1.12  A  per  bushel,  will 
pay  for  900  bushels  of  corn  at  one  dollar  per  bushel  ? 

38 Jf.  Add  5  dollars,  5  cents,  5  mills ;  seventy  dollars,  7  mills ; 
nine  dollars,  eight  cents,  six  mills;  and  three  dollars,  four 
cents,  two  mills. 

885.  If  42  cords  of  wood  cost  $136.50,  what  cost  28  cords  ? 

886.  A  lady  having  $75  spent  $46.37A  in  shopping ;  how 
much  was  left  ? 

887.  A  man  buys  a  horse  for  $355.12A,  and  gives  in  pay- 
ment a  five  hundred  dollar  bill ;  how  much  should  he  receive 
back? 

388.  What  cost  525  bales  of  cloth  at  $472.25  per  bale  ? 

389.  At  $7.63  per  barrel,  how  many  barrels  of  flour  can  be 
purchased  for  $5180.77  ? 

390.  If  123  tons  of  coal  cost  $848.70,  what  will  be  the  cost 
of  265  tons  ? 

891.  A  person  having  bought  a  bill  of  goods  amounting  to 
$87.12 J,  gave  in  payment  a  hundred  dollar  bill;  how  much 
change  did  he  receive  ? 

892.  At  twenty-four  dollars  and  five  cents  a  ton,  how  much 
will  95  tons  of  hay  cost  ? 

893.  If  250  barrels  of  flour  cost  $1312.50,  what  is  the  price 
per  barrel  ? 

894.  If  29  bushels  of  corn  cost  $36,308,  what  is  the  price 
per  bushel  ? 

895.  How  much  must  you  add  to  $62.37}  to  make  $100  ? 

896.  If  12  cords  of  wood  cost  $90,  what  will  50  cords  cost  ? 

397.  A  man  had  $600;  he  bought  a  horse  for  $225,  a  car- 
riage for  $190.12,  and  a  harness  for  $40  and  5  mills;  how 
much  had  he  left  ? 


CHAP.  x\y  AEITHMETICAL  EXAMPLES.  21 

898.  Eeduce  16  T.  2  cwt.  75  lb.  7  oz.  to  ounces. 

399.  Eeduce  917482  grains  Troy  to  pounds. 

400.  How  many  grains  in  7  K>  5  f  6  3  2  3  10  gr.  ? 
4W.  In  21  lb.  9  oz.  4  pwt.  15  gr.,  bow  many  grains  ? 
J/02.  In  217532  grains  Apothecaries,  how  many  pounds  ? 

403.  Change  472  lb.  10  oz.  14  pwt.  to  pennyweights. 

404.  Change  378641  lbs.  to  tons. 

405.  Change  19  lb.  4  oz.  11  pwt.  15  gr.  to  grains. 

406.  In  865904  grains  Apothecaries,  how  many  pounds  ? 

407.  Reduce  57  T.  11  cwt.  48  lb.  12  oz.  to  ounces. 

408.  In  563427  ounces,  how  many  tons  ? 

409.  How  many  lbs.  Troy  in  517823  grains  ? 

410.  How  many  lbs.  in  37  T.  19  cwt.  75  lb.  ? 
If  11.  In  450325  oz.,  how  many  tons  ? 

412.  How  many  pounds  in  142524  pennyweights  ? 

413.  Eeduce  12  ft,  8  3  5  3  2  3  to  grains  ? 

414.  In  4753814  oz.,  how  many  tons  ? 

415.  Eeduce  5  T.  3  cwt.  71  lb.  to  ounces. 

416.  In  74867  scruples,  how  many  pounds  ? 

417.  Change  144  lb.  11  oz.  Apothecaries  to  drams. 

418.  How  many  cwt.  in  436287  ounces  ? 

419.  Eeduce  37  lb.  6  oz.  13  pwt.  19  gr.  to  grains. 

420.  Eeduce  40  T.  5  cwt.  24  lb.  to  ounces. 
42t  Eeduce  1274215  grains  Troy  to  lbs. 

422.  In  25  T.  15  cwt.,  how  many  pounds  ? 

423.  In  9  lb.  10  oz.  17  pwt.,  how  many  grains  ? 
J$4-  How  many  scruples  in  23  lb.  ? 

425.  How  many  lb.  of  hay  in  5  T.  97  lb.  ? 

426.  Eeduce  12  lb.  5  oz.  10  pwt.  to  grains. 

427.  How  many  grains  in  a  gold  pitcher  weighing  4  lb.  ? 

428.  How  many  pounds  in  23040  grains  Troy  ? 

429.  How  many  lbs.  of  sugar  in  a  box  containing  3  T.  5  cwt.  ? 

430.  In  8  5  5  3  2  3  10  gr.,  how  many  grains  ? 

431.  Eeduce  9870  3  to  higher  denominations. 
In  7  lb.  3  oz.  10  pwt.  20  gr.,  how  many  grains  ? 
Eeduce  12  T.  4  cwt.  24  lb.  15  oz.  to  ounces. 

4&4-  How  many  oz.  in  a  bale  of  cotton  weighing  395  lb.  ? 
435.  How  many  gr.  in  a  silver  cup  weighing  9  oz.  18  pwt.  ? 


22  AEITHMETICAL  EXAMPLES.  [CHAP.  I. 

436.  Reduce  6  m.  214  rd.  4  yd.  to  inches. 

437.  Reduce  18  C.  5  c.  ft.  12  cu.  ft.  429  cu.  in.  to  cubic  inches. 

438.  How  many  links  in  7  m.  4  cha.  5  rd.  ? 

439.  How  many  sq.  in.  in  12  A.  137  sq.  rd.  ? 
JfJfO.  Change  69473541  sq.  in.  to  acres. 

441.  Required  the  number  of  yards  in  96  m.  124  rd. 

442.  Reduce  7  m.  127  rd.  13  ft.  to  inches. 

443*  Required  the  number  of  miles  in  546729  inches. 

444'  Change  17  cords  43  cu.  ft.  to  cubic  inches. 

44$-  Change  17  cords  2  c.  ft.  12  cu.  ft.  to  cubic  inches. 

446.  Reduce  54  A.  129  rd.  to  square  yards. 

447.  Reduce  4375672  cu.  in.  to  cords. 
443*  Reduce  35  m.  125  rd.  2  yd.  to  inches. 

449*  Find  the  number  of  cords  in  754367  inches. 

450.  How  many  miles  in  51708443  sq.  ft.  ? 

451.  Required  the  number  of  links  in  78  m.  9  ch.  15  1. 

452.  Reduce  470  rods,  4  yds.  2  ft.  11  in.  to  inches. 

453.  How  many  sq.  rods  in  1574753  sq.  in.  ? 

45 4-  In  8  m.  97  rd.  5  yd.  3  ft.  9  in.,  how  many  inches  ? 

455.  Change  5764986  cu.  in.  to  cubic  yards. 

456.  Reduce  21  sq.  mi.  3  A.  39  sq.  rd.  to  sq.  ft 

457.  Reduce  88794763  in,  to  higher  denominations. 

458.  Change  10  mi.  8  ch.  to  links. 

459.  Reduce  27  m.  232  rd.  13  ft.  9  in.  to  inches. 

460.  Reduce  15342174  in.  to  cords. 

461.  Reduce  453726  sq.  in.  to  higher  denominations. 

462.  How  many  sq.  yds.  in  5  A.  120  rd.  ? 

468.  How  many  cu.  in.  in  40  C.  6  c.  ft.  12  cu.  ft.  ? 
464  Reduce  8  mi.  3  yd.  2  ft.  6  in.  to  inches. 

465.  Change  3  A.  5  sq.  rd.  12  sq.  yd.  2  sq.  ft  to  sq.  in. 

466.  Change  123456  sq.  in.  to  higher  denominations. 

467.  How  many  cu.  in.  in  4  C.  3  c.  ft.  12  cu.  ft.  1000  cu.  in.  ? 

468.  Reduce  35678  ft  to  higher  denominations. 

469.  Reduce  763456  in.  to  higher  denominations. 

470.  In  12  C.  100  cu.  ft  728  cu.  in.,  how  many  cubic  inches  ? 

471.  How  many  sq.  feet  in  50  miles  ? 

472.  Change  79846  sq.  yd.  to  higher  denominations. 
478.  Reduce  25  mi.  315  rd.  4  yd.  to  feet. 


ARITHMETICAL  EXAMPLES.  23 

474.  Reduce  12  bu.  3  pk.  3  qt.  1  pt  to  pints. 

475.  Reduce  894324  gills  to  gallons. 
4.76.  How  many  cords  in  452382  cu.  ft.  ? 

477.  How  many  square  feet  in  2  A.  115  sq.  rd.  200  sq.  ft.  ? 

478.  Eeduce  4  mi.  213  rd.  15  ft  to  inches. 

479.  How  many  ounces  in  5  T.  2  cwt.  20  lb.  ? 

480.  Reduce  38  ft>  3  §  2  3  2  3  5  gr.  to  grains. 

481.  How  many  grains  in  35  lb.  11  oz.  16  pwt. 

482.  Reduce  497812  farthings  to  higher  denominations. 

483.  Reduce  7386541  pwt.  to  higher  denominations. 
484-  Reduce  296814  scruples  to  higher  denominations. 

485.  2863458  oz.  Avoirdupois  to  higher  denominations. 

486.  How  many  inches  in  50  mi.  37  rd.  12  ft.  4  in.  ? 

487.  In  5229428  links  how  many  miles,  chains,  etc.  ? 

488.  Reduce  12  cu.  yd.  8  cu.  ft.  376  cu.  in.  to  inches. 

489.  How  many  gallons  in  32684  gills  ? 

490.  Reduce  315°  42'  18"  to  seconds. 

491.  How  many  minutes  in  5  y.  7  mo.  4  da.  9  h.  ? 

492.  Reduce  60  gal.  3  qt.  1  pt.  to  gills. 

493.  Reduce  512473  sq.  ft.  to  yds.,  etc. 

494-  In  391652  oz.,  how  many  lbs.,  cwt,  etc.  ? 

495.  Reduce  9  lb.  6  oz.  2  sc.  15  gr.  to  grains. 

496.  In  57  lb.  6  oz.  0  pwt  13  gr.,  how  many  grains  ? 

497.  How  many  farthings  in  £43  10s.  lid.  ? 

498.  Reduce  864325  grains  Troy  to  higher  denominations, 

499.  In  8  T.  15  cwt.  76  lb.,  how  many  ounces  ? 

500.  How  many  square  miles,  etc.,  in  5721432  sq.  in.  ? 

501.  In  25  mi.  30  rd.  14  ft,  how  many  inches  ? 

502.  Reduce  4  m.  16  cha.  3  1.  to  links. 

503.  How  many  sq.  ft.  in  30  A.  130  rd.  and  200  sq.  ft.  ? 
504*  In  3756243  cu.  in.,  how  many  cords  ? 

505.  Reduce  57  gal.  3  qt.  0  pt.  3  gi.  to  gills. 

506.  How  many  degrees  in  47295  seconds  ? 

507.  How  many  guineas  in  57684  pence  ? 

508.  In  46  lb.  10  pwt.  15  gr.,  how  many  grains  ? 

509.  Reduce  7324251  ounces  to  tons,  etc. 

510.  Reduce  6249687  sq.  in.  to  higher  denominations. 

511.  Reduce  15472  links  to  higher  denominations. 


24  ARITHMETICAL  EXAMPLES.  [CHAP.  I. 

512.  What  is  the  value  of  15  lb.  of  gold  at  4  cts.  per  gr.  ? 

518.  What  is  the  value  of  19  bu.  of  beans  at  12}  cts.  per 
qt? 

5U.  How  many  quart  boxes  will  be  required  to  hold  78 
bu.  1  pk.  6  qt.  of  grapes  ? 

515.  Kequired  the  price  of  1  T.  14  cwt.  16  lb.  of  butter  at 
3  cts.  per  oz.  ? 

516.  How  many  cords  of  wood  in  a  pile  132  ft.  long,  24  ft. 
wide,  and  14  ft.  high  ? 

517.  At  $.015  a  pound  what  will  be  the  cost  of  30  T.  15 
cwt  of  hay  ? 

518.  How  many  half-pint  bottles  are  required  to  hold  725 
gal.  2  qt.  of  wine  ? 

519.  If  1  oz.  of  sugar  cost  1  ct.  what  will  be  the  cost  of  5  T. 
9  cwt.  75  lb.  ? 

520.  How  many  times  can  you  fill  a  half  bushel  measure 
from  15872  pints  ? 

521.  What  is  the  value  of  3  doz.  silver  spoons,  each  weigh- 
ing 2  oz.,  at  4  cts.  a  pwt.  ? 

522.  How  many  minutes  in  the  month  of  February,  1872  ? 
528.  What  is  the  cost  of  a  field  containing  128  acres,  at  25 

cts.  per  rd.  ? 

521f.  In  a  pile  of  wood  117  ft  long,  15  ft  wide,  and  12  ft 
high,  how  many  cords  ? 

525.  How  many  townships,  each  6  miles  square,  in  967680 
acres  ? 

526.  What  will  be  the  cost  of  560  gallons  of  vinegar  at  2 
cts.  per  gill  ? 

527.  How  many  acres  in  a  farm  225  rds.  long  and  175  rds. 
wide? 

528.  How  much  will  it  cost  to  carpet  a  room  18  ft.  long 
and  15  ft.  wide,  at  $2.35  per  yd.  ? 

529.  How  many  cubic  feet  in  a  room  18  ft.  long  by  17  ft. 
wide  and  15  ft  high  ? 

580.  How  many  square  ft.  in  the  walls  of  the  above  room  ? 


CHAP.   I.]  ARITHMETICAL   EXAMPLES.  25 

531.  How  many  yards  in  a  garden  78  ft.  long  and  72  ft. 
wide  ? 

532.  When  gold  is  worth  $.96  a  pwt.  what  is  the  value  of 
6  lb.? 

533.  How  many  acres  in  25  townships,  each  6  miles  square  ? 

534.  How  many  acres  in  25  townships,  each  containing  6 
square  miles  ? 

535.  What  is  the  cost  of  4  T.  85  lb.  of  lead  at  7  mills  per 
oz.  ? 

536.  How  many  cubic  yards  must  be  removed  in  digging  a 
ditch  423  ft.  long,  6  ft.  wide,  and  3  ft.  deep  ? 

537.  How  many  doz.  eggs  at  25  cts.  per  doz.  will  pay  for  2 
T.  1  cwt.  26  lb.  of  sugar,  at  $.125  a  pound  ? 

538.  How  many  pounds  of  rice  at  12  cts.  a  pound  will  pay 
for  4  bu.  2  pk.  of  nuts  at  8  cts.  a  pint  ? 

539.  How  many  tons  of  timber  at  $12  per  ton  will  pay  for 
15  T.  9  cwt.  of  cotton  at  16  cts.  a  pound  ? 

540.  Bought  130  gallons  of  molasses  for  $60,  and  retailed  it 
at  10  cts.  a  pint.    How  much  was  gained  ? 

54L  How  many  jars  will  be  required  to  hold  2  T.  5  cwt.  of 
butter,  if  1  jar  will  hold  50  lb.  ? 

542.  What  is  the  value  of  5  cwt.  12  lb.  of  gum  Arabic  at  4 
cts.  per  oz.  ? 

543.  What  cost  a  pile  of  wood  40  ft.  long,  12  ft.  wide,  and 
4  ft.  high,  at  $8  per  cord  ? 

544.  If  1  qt.  of  nuts  costs  12  cts.,  how  many  bushels  can  be 
purchased  for  $25.08  ? 

545.  How  many  doses  of  medicine  of  15  gr.  each  in  2 
pounds  ? 

546.  What  will  it  cost  to  dig  a  cellar  21  ft.  long,  18  ft.  wide, 
and  6  ft.  deep,  at  30  cts.  a  yard  ? 

547.  What  cost  a  tract  of  land  5  miles  square,  at  $20  per 
acre? 

548.  If  it  requires  9  oz.  of  silver  to  make  a  cup,  how  many 
cups  can  be  made  from  36  lb.  ? 

2 


26  ARITHMETICAL   EXAMPLES.  [CHAP.  I. 

549.  What  is  the  sum  of  £36  15s.  6<L;  £52  4s.  6d.;  £75 
12s.  lid.;  £425  10s.  10d.;  £17  5s.  4d.  ? 

550.  Add  4  lb.  11  oz.  12  pwt.  8  gr. ;  9  lb.  10  oz.  15  pwt.  6 
gr. ;  16  lb.  9  oz.  7  pwt.  12  gr. ;  20  lb.  6  oz.  13  pwt.  20  gr. 

551.  What  is  the  difference  between  25  lb.  6  oz.  3  dr.  2  sc., 
and  12  lb.  9  oz.  6  dr.  15  gr.  ? 

552.  Find  the  sum  of  8  T.  16  cwt.  12  lb.  14  oz. ;  12  T.  4  cwt. 
18  lb.;  5  T.  13  cwt.  9  oz. ;  57  T.  23  lb.  13  oz.;  19  cwt.  17  lb. 
8oz. 

553.  How  many  cords  in  four  piles  of  wood  measuring  as 
follows:  18  cd.  13  cu.  ft.;  12  cd.  7  cd.  ft.;  21  cd.  4  cu.  ft.; 
65  cd.  15  cu.  ft.  ? 

654.  Add  57  A.  25  rd.  15  yd.;  129  A.  18  rd.;  37  A.  50  rd. 
13  yd. ;  75  A.  12  yd. ;  35  rd.  10  yd. 

555.  Find  the  time  from  May  4th,  1867,  to  March  1st, 
1871. 

556.  Add  15  cwt.  19  lb.  14  oz.;  172  T.  12  lb.  10  oz. ;  13  cwt 
7  lb.  5  oz. ;  45  T.  11  cwt.  10  oz. ;  29  T.  15  cwt  17  lb.;  14  cwt 
21  lb.  12  oz. 

557.  Subtract  8  bu.  3  pk.  7  qt.  1  pt.  from  47  bu.  1  pk. 
5  qt. 

558.  Add  30°  45' 14";  27°  15' 40";  16°  12'  50";  21°  42"; 
18'  40". 

559.  From  37  T.  12  cwt  take  19  T.  14  cwt.  20  lb.  9  oz. 

560.  Find  the  time  from  March  7,  1865,  to  February  20, 
1870. 

561.  Add  125  gal.  3  qt.  1  pt.  2  gi.;  75  gal.  2  qt.  1  pt.  3  gi.; 
45  gal.  3  qt.  2  gi. ;  39  gal.  1  qt.  1  pt. ;  250  gal.  2  qt.  1  pt. 

662.  What  is  the  sum  of  39  mi.  36  rd.  15  ft  4  in. ;  50  mi. 
25  rd.  12  ft. ;  27  rd.  9  ft.  11  in. ;  500  mi.  35  rd.  11  ft.  9  in.  ? 

568.  From  a  pile  of  wood  containing  29  cords  I  sold  12  cd. 
5  cd.  ft.  12  cu.  ft    How  much  remained  ? 

664.  Add  43  A.  32  rd.  127  ft. ;  240  A.  20  rd.  200  ft. ;  95  A. 
25  rd.  75  ft. ;  12  A.  100  ft;  137  rd.  30  ft. 

665.  From  100  mi.  take  36  rd.  2  yd.  1  ft.  10  in. 

666.  Required  the  time  from  July  4,  1867,  to  May  2, 187?, 


CHAP.  I.]  ARITHMETICAL  EXAMPLES.  27 

567.  How  much  wood  is  there  in  three  piles,  the  first  of 
Which  contains  12  cd.  4  cd.  ft.  7  cu.  ft.,  the  second  9  cd.  12 
cu.  ft.,  and  the  third  20  cd.  6  cd.  ft  5  cu.  ft.  ? 

568.  A  note  dated  June  12,  1868,  was  paid  September  3, 
1871.    How  long  did  it  remain  unpaid  ? 

569.  Add  15  bu.  3  pk.  6  qt.;  9  bu.  4  qt.  1  pt. ;  2  pk.  5  qt, 
1  pt. ;  30  bu.  1  pk.  3  qt.  1  pt. 

570.  Eequired  the  time  from  December  14, 1799,  to  January 
1,  1872. 

571.  Find  the  sum  of  42  A.  137  rd.  5  yd.;  17  A.  27  yd.; 
20  A.  96  rd.  12  yd. ;  45  A.  113  rd.  16  yd. 

572.  Eequired  the  time  from  February  22,  1732,  to  Decem- 
ber 14, 1799. 

573.  The  latitude  of  New  York  is  N.  40°  42'  40".  Port- 
land N.  43°  39'.    What  is  the  difference  ? 

57 Jj..  Washington  is  77°  2'  W.  Ion.  St.  Louis  89°  36'  W. 
Ion.    Eequired  the  difference. 

575.  Boston  is  42°  21'  22"  N.  lat.  Buenos  Ayres  34°  36' 
S.  lat.    What  is  the  difference  ? 

576.  Chicago  is  in  42°  N.  lat.  New  Orleans  nearly  30°  N. 
lat.    Eequired  the  difference. 

577.  The  longitude  of  Boston  is  71°  W.  San  Francisco 
122°  W.    What  is  the  difference  ? 

578.  Constantinople  is  in  41°  N.  lat.  St.  Petersburg  60°  N. 
lat.    What  is  the  difference  in  miles  ? 

579.  Washington  is  38°  53'  23"  N.  lat.  Montreal  45°  31'. 
Eequired  the  difference. 

580.  New  York  is  74°  W.  Ion.  Eome  12°  28'  40"  E.  Ion. 
What  is  the  difference  ? 

581.  Portland  is  70°  20'  W.  Ion.  Cairo  31°  E.  Ion.  What 
is  the  difference  ? 

582.  Havana  is  82°  22'  W.  Ion.  Detroit  82°  58'.  What  is 
the  difference  ? 

583.  How  many  square  inches  in  three  boards,  the  first 
measuring  15  ft.  10  in.,  the  second  21  ft.  9  in.,  and  the  third 
27  ft.  4  in.  ? 


28  AKITHMETICAL   EXAMPLES.  [CHAP.   L 

584..  Multiply  45  bu.  3  pk.  6  qt.  1  pt.  by  15. 

585.  Divide  18  lb.  3  oz.  15  pwt.  8  gr.  by  4. 

586.  What  is  the  product  of  £27  15s.  lid.  2qr.  multiplied 
by  8? 

587.  Find  the  quotient  of  57  mi.  4  rd.  12  ft.  divided  by  6. 

588.  Multiply  37  T.  12  cwt.  5  lb.  9  oz.  by  12. 

589.  Find  the  product  of  3  w.  6  da.  11  h.  27  m.  47  sec.  x  lL 

590.  Divide  212  mi.  26  rd.  2  yd.  by  7. 

591.  Divide  143  bu.  2  pk.  2  qt.  1  pt.  by  9. 

592.  Required  the  product  of  2  T.  5  cwt.  20  lb.  13  oz.  x  9. 

593.  Required  the  quotient  30  bu.  3  pk.  6  qt.  1  pt.  —  11. 

594.  Divide  131  lb.  2  oz.  15  pwt.  20  gr.  by  50. 

595.  What  is  the  product  of  16  A.  125  rd.  multiplied  by  12  ? 

596.  How  many  times  is  8  contained  in  £185  17s.  6d.  ? 

597.  Multiply  38  cd.  54  cu.  ft.  143  in.  by  5. 

598.  Divide  34  A.  32  rd.  8  yd.  5  ft.  48  in.  by  12. 

599.  How  many  times  is  8  contained  in  21  T.  5  cwt.  21  lb.  ? 

600.  Multiply  12  mi.  37  rd.  4  yd.  2  ft.  9  in.  by  15. 

601.  Find  the  quotient  of  £147  17s.  4d.  2qr.  -f-  24. 

602.  Divide  43  cd.  4  cd.  ft.  11  cu.  ft.  1512  in.  by  18. 

603.  Multiply  17  y.  27  da.  22  h.  30  m.  40  sec.  by  12. 

604.  What  is  the  product  of  9  mi.  30  rd.  4  yd.  2  ft.  6  in.  x  6  ? 

605.  What  is  the  quotient  of  427  lb.  11  oz.  18  pwt  19 
gr. -27? 

606.  Multiply  87  lb.  8  oz.  19  pwt.  21  gr.  by  3. 

607.  Multiply  3  mi.  38  rd.  4  yd.  11  in.  by  3. 

608.  Required  the  quotient  5  mi.  75  A.  24  rd.  -f-  2. 

609.  Divide  17  A.  21  rd.  20  yd.  5  ft.  by  11. 

610.  Required  the  product  of  19  lb.  7  oz.  5  dr.  2  sc.  x  8. 

611.  Multiply  £17  19s.  9d.  3qr.  by  7. 

612.  Divide  3  T.  4  cwt.  6  lb.  12  oz.  by  7. 
618.  Multiply  20  mi.  25  rd.  15  ft.  by  9. 

614.  What  is  the  quotient  of  28  gal.  3  qt  1  pt  2  gi.  ^  6  ? 

615.  Required  the  product  of  5  lb.  3  oz.  18  pwt.  x  5. 

616.  Divide  19  T.  7  cwt.  14  lb.  10  oz.  by  6. 

617.  Multiply  20  A.  30  rd.  15  yd.  6  ft.  by  5. 

618.  Divide  8  cd.  3  cd.  ft.  8  cu.  ft.  by  5. 

619.  Multiply  3  w.  2  da.  5  h.  35  m.  49  sec.  by  4. 


CHAP.   I.]  AKITHMETICAL   EXAMPLES.  29 

620.  A  silversmith  bought  a  lot  of  gold  weighing  2  lb.  6  oz. 
12  pwt.  for  $550  and  sold  it  at  5  cents  a  gr.  How  much  did 
he  gain  ? 

621.  How  many  yards  in  the  four  walls  of  a  room  36  ft. 
long,  24  ft.  wide,  and  12  ft.  high  ? 

622.  How  many  cubic  feet  in  the  above  room  ? 

623.  How  much  will  it  cost  to  carpet  the  above  room  at 
$1.75  per  square  yard  ? 

62^.  Bought  8  casks  of  wine,  each  containing  36  gal  3  qt., 
at  2  cents  a  pint.    How  much  did  it  cost  ? 

625.  How  many  bales,  each  weighing  375  lb.,  will  36  T.  3 
cwt.  75  lb.  of  hay  make  ? 

626.  A  gardener  sold  9  bu.  2  pk.  2  qt.  of  strawberries  at  32 
cents  per  quart.    How  much  did  he  receive  ? 

627.  A  fruit  dealer  sold  649  baskets  of  peaches  for  $1590.05. 
What  was  the  price  per  basket  ? 

628.  How  many  yards  of  cloth  at  $.20  per  yard  will  pay  for 
5  barrels  of  cranberries,  each  containing  2  bu.  3  pk.,  at  $.17 
per  quart  ? 

629.  How  many  cases  of  boots  at  $40  per  case  will  pay  for 
15  T.  12  cwt.  60  lb.  of  rice  at  8  cents  a  pound  ? 

630.  If  $39.48  are  paid  for  28  bushels  of  wheat,  what  must 
be  paid  for  48  bushels  ? 

631.  Bought  5  T.  11  cwt.  of  iron  at  7  cents  a  pound.  How 
many  cords  of  wood  at  $3.50  per  cord  will  pay  for  the  iron  ? 

632.  Name  the  leap  years  between  1871  and  1900. 

633.  Bought  a  wood  lot  containing  4  A.  90  rd.  at  33  cents  a 
rod,  and  paid  for  it  with  wood  at  $8.03  per  cord.  How  many 
cords  did  it  take  ? 

634.  If  200  lb.  of  pork  are  worth  $19,  what  are  540  lb. 
worth  ? 

635.  How  many  farms  of  80  acres  each  are  contained  in  a 
township  6  miles  square  ? 

636.  How  many  cords  of  bark  at  $12.50  per  cord  will  pay 
for  2  T.  15  cwt.  of  leather  at  20  cents  a  pound  ? 


30  AKITHMETICAL    EXAMPLES.  [CHAP.  I. 

687.  "What  is  the  cost  of  25  reams  6  quires  15  sheets  of 
paper,  at  1  cent  a  sheet  ? 

688.  How  many  seconds  in  the  month  of  January  ? 

639.  How  many  feet  in  a  room  30  ft.  long,  24  ft.  wide,  and 
15  ft.  high? 

640.  What  will  it  cost  to  plaster  the  walls  of  the  above  room 
at  $.20  per  yard  ? 

641.  How  much  will  it  cost  to  plaster  the  ceiling  at  25  cents 
a  yard  ? 

642.  What  cost  a  pile  of  wood  55  ft.  long,  12  ft.  wide,  and 
20  ft.  high,  at  1  dollar  per  cord  feet  ? 

643.  How  much  rice  at  8  cents  a  pound  will  pay  for  5  bu. 

3  pk.  of  cherries  at  9  cents  per  quart  ? 

644.  Required  the  time  from  November  21, 1868,  to  June 
16,  1871. 

645.  If  328  pounds  of  tea  cost  $249.28,  what  will  455  pounds 
cost? 

646.  If  a  man  travel  317  mi.  140  rd.  in  fifteen  days,  how  far 
will  he  travel  in  1  day  ? 

647.  How  many  bushels  of  oats  will  a  span  of  horses  eat  in 

4  weeks,  if  they  eat  24  quarts  a  day  ? 

648.  How  many  cords  of  wood  at  $9.50  per  cord,  will  pay 
for  76  yd.  of  cloth  at  $2.50  per  yd.  ? 

649.  What  is  the  sum  of  the  following  distances :  5  mi.  15 
rd.  4  yd. ;  12  mi.  30  rd.  2  ft. ;  2  mi.  36  rd.  2  ft. ;  15  mi. 
37  rd.? 

650.  If  1  acre  of  land  produce  1  T.  19  cwt.  21  lb.  of  hay, 
what  will  5  acres  produce  ? 

651.  How  many  cubic  yards  in  a  cellar  42  ft.  long,  24  ft. 
wide,  and  6  ft.  deep  ? 

652.  How  many  barrels  of  flour  at  $8.75  per  barrel,  will  pay 
for  30  T.  12  cwt.  of  hops  at  45  cents  a  pound  ? 

653.  A  school-room,  36  ft.  long  by  30  ft  wide  and  18  ft. 
high,  contains  how  many  feet  of  ail  ? 

654.  How  much  will  it  cost  to  plaster  the  above  room  at  22 
cents  per  yard ;  deducting  100  yards  for  windows,  doors,  &c.  ? 


CHAPf  IB.  II, 

COMMON  AND  DECIMAL  FRACTIONS,  WITH  A  REVIEW  OF 
ALL  PRECEDING  SUBJECTS. 

Required  the 

1.  Greatest  common  divisor  of  198,  297,  and  99. 

2.  Least  common  multiple  of  48,  20,  21,  and  12. 

3.  Greatest  common  divisor  of  864,  420,  and  12. 

If..  Least  common  multiple  of  8,  24,  32,  48,  and  96. 

5.  Greatest  common  divisor  of  96,  264,  and  48. 

6.  Least  common  multiple  of  15,  8,  11,  and  5. 

7.  Greatest  common  divisor  of  18,  30,  and  48. 

8.  Least  common  multiple  of  24, 180,  45,  60,  and  15. 

9.  Greatest  common  divisor  of  36,  108,  and  252. 

10.  Least  common  multiple  of  36,  24,  48,  72,  and  30. 

11.  Greatest  common  divisor  of  6,  9,  4,  and  16. 

12.  Least  common  multiple  of  16,  28,  63,  and  35. 

13.  Greatest  common  divisor  of  24,  96,  and  144. 
lJf.  Least  common  multiple  of  8, 10,  18,  and  25. 

15.  Greatest  common  divisor  of  120,  144,  and  168. 

16.  Least  common  multiple  of  13,  39,  56,  and  63. 

17.  Greatest  common  divisor  of  77, 132,  and  154. 

18.  Least  common  multiple  of  5,  12,  9,  15,  and  18. 

19.  Greatest  common  divisor  of  75,  225,  and  450. 

20.  Least  common  multiple  of  40,  28,  32,  6,  and  4. 

21.  Greatest  common  divisor  of  16,  24,  and  36. 

22.  Greatest  common  divisor  of  108,  63,  and  45. 

23.  Least  common  multiple  of  99,  11,  13,  and  26. 
21/..  Greatest  common  divisor  of  66,  154,  and  220. 

25.  Least  common  multiple  of  5,  16,  24,  and  32. 

26.  Greatest  common  divisor  of  315,  945,  and  63. 

27.  Least  common  multiple  of  4,  5,  6,  7,  and  8. 


32  ARITHMETICAL   EXAMPLES.  [CHAP.   II. 

28.  Reduce  Jf|  to  its  lowest  terms. 

29.  Reduce  I$|*  to  a  mixed  number. 
SO.  Reduce  84 \ \  to  an  improper  fraction. 
31.  Reduce  ^s  to  its  lowest  terms. 

82.  Reduce  79f -§  to  an  improper  fraction. 
S3.  Reduce  -f  of  f  of  §  to  a  simple  fraction. 
SJf.  Reduce  *||  A-  to  a  mixed  number. 

35.  Reduce  %  %  §  to  its  lowest  terms. 

36.  Reduce  *|§*  to  a  mixed  number. 

37.  Reduce  §  of  \  of  J  to  a  simple  fraction. 

38.  Reduce  264§  §  to  an  improper  fraction. 

39.  Reduce  |||  to  its  lowest  terms. 
Jfi.  Reduce  -4T8T2-  to  a  mixed  number. 

41.  Reduce  ■$  of  §  of  $  to  a  simple  fraction. 

42.  Reduce  721  \\  to  an  improper  fraction. 
J/3.  Reduce  £\6^-  to  a  mixed  number. 

44'  Reduce  -f  |-  to  a  mixed  number. 

45.  Reduce  }$$  to  its  lowest  terms. 

46.  Reduce  87  ^  to  an  improper  fraction. 

47.  Reduce  \  of  %  of  |  to  a  simple  fraction. 

48.  Reduce  -%%&  to  a  mixed  number. 

49.  Reduce  73  j  to  an  improper  fraction. 

50.  Reduce  ^  of  jj  of  \  to  a  simple  fraction. 

51.  Reduce  598?  to  an  improper  fraction. 

52.  Reduce  ffo  to  its  lowest  terms. 

53.  Reduce  ij|£  to  a  mixed  number. 

54.  Reduce  f g§  to  its  lowest  terms. 

55.  Reduce  425-,-%  to  an  improper  fraction. 

56.  Reduce  ±§|A  to  a  mixed  number. 

57.  Reduce  |  to  twenty-fourths. 

58.  Reduce  |^|  to  its  lowest  terms. 

69.  Reduce  492  }-§  to  an  improper  fraction. 

60.  Reduce  5  and  §  to  thirty-fifths. 

61.  Reduce  §  of  T53  of  |  to  a  simple  fraction. 

62.  Reduce  &|$£  to  a  mixed  number. 

63.  Reduce  469T\  to  an  improper  fraction. 

64.  Reduce  321  to  fifths. 

65.  Reduce  519  to  sevenths. 


CHAP.  II.]  ARITHMETICAL  EXAMPLES.  33 

66.  Reduce  f ,  ?,  J  to  the  least  common  denominator. 

67.  Reduce  |j,  j,  J,  |  to  the  least  common  denominator. 

68.  Reduce  I,  §,  J,  §  to  the  least  common  denominator. 
00.  Reduce  T\,  -/v,  24-  to  the  least  common  denominator. 

70.  Reduce  3,  -] -£,  -J,  g  to  the  least  common  denominator. 

71.  Reduce  fa  §,  f,  \  to  the  least  common  denominator. 

72.  Reduce  j,  |,  and  f  to  the  least  common  denominator. 

78.  Reduce  5^,  T%,  335,  -A%  to  the  least  common  denom. 

74.  Reduce  ^fa  52/r,  -3D24  to  the  least  common  denom. 

75.  Reduce  ffly,  j§  to  the  least  common  denominator. 

76.  Reduce  /ff,  {£,  T8g  to  the  least  common  denominator. 

77.  Reduce  fa,  fj,  ■&,  ¥8r  to  the  least  common  denom. 
75.  Reduce  £  and  f  of  |  to  the  least  common  denom. 

79.  Reduce  £,  |,  j  to  the  least  common  denominator. 
£0.  Reduce  3,  yV,  o5T  to  the  least  common  denominator. 
81.  Reduce  fa  ^,  T5.j  to  the  least  common  denominator. 
£#.  Reduce  \,  §,  3},  A  to  the  least  common  denominator. 
£$.  Reduce  f ,  J,  J,  -j%  to  the  least  common  denominator. 
8J+.  Reduce  9,  |,  -fa  %,  %  to  the  least  common  denom. 

85.  Reduce  f,  f,  jj,  J,  |  to  the  least  common  denom. 

86.  Reduce  -fa  § ,  760,  |  to  the  least  common  denom. 

87.  Reduce  4,  f >  J  to  the  least  common  denominator. 

88.  Reduce  T'g,  -f,  §,  \  to  the  least  common  denominator. 
£P.  Reduce  T%,  J,  |,  3%  to  the  least  common  denom. 

90.  Reduce  T4-,  T5T,  ££  to  the  least  common  denominator. 

91.  Reduce  T|,  f,  T30,  J  to  the  least  common  denominator. 

92.  Reduce  |,  J,  f,  §  to  the  least  common  denominator. 

93.  Reduce  f,  §,  j,  f  to  the  least  common  denominator. 
91/..  Reduce  §,  f,  §,  J  to  the  least  common  denominator. 

95.  Reduce  Ij,  £,  f,  |  to  the  least  common  denominator. 

96.  Reduce  fa,  fa  ffa  £  to  the  least  common  denom. 

97.  Reduce  j,  f ,  TG2,  |  to  the  least  common  denominator. 

98.  Reduce  fa  ^2,  }|  to  the  least  common  denominator. 

99.  Reduce  4g,  fa  fa,  £  to  the  least  common  denom. 

100.  Reduce  \£,  },  fa  F\  to  the  least  common  denom. 

101.  Reduce  £,  J,  fa,  §  to  the  least  common  denominator. 

102.  Reduce  4,  ||>  25  to  the  least  common  denominator. 

103.  Reduce  f  J,  §,  T83  to  the  least  common  denominator. 

2* 


34  AKITHMETICAL   EXAMPLES.  [CHAP.   E 

104.  Find  the  sum  of  -ft,  £f ,  T83,  and  §. 

105.  Required  the  difference  between  \l  and  T^. 

106.  Add  together  $,  $,  J,  and  f\. 

i07.  Required  the  difference  between  }f  and  {§. 

m?.  Find  the  sum  of  f,  7\,  £,  and  1  J. 

16$.  Required  the  difference  between  j|  and  }$. 

Jtf0.  Addf  +  |  +  |  +  |. 

/IL  Subtract  $  of  T%  from  f . 

112.  Add  together  6f,  5J,  and  4|. 

li&  Find  the  difference  between  Jf  and  f  f. 

H£.  Required  the  amount  of  2|,  3-£,  and  7 \. 

115.  Subtract  15|  from  328§. 

116.  Required  the  sum  of  J  + 1 + 4  4-  7V 

117.  Required  the  difference  between  T9T  and  {§. 

118.  Add  together  12f,  15|,  and  30§. 

119.  Subtract  75f  from  90. 

120.  Find  the  sum  of  ^  f>  A>  and  J- 

i#l.  Required  the  difference  between  40f  and  5&J. 

122.  Find  the  sum  of  f  of  f  and  J  of  j. 

1#&  Find  the  difference  between  }§  and  f  §. 

m.  Aad|,},4f,attdi|. 

125.  Subtract  24|  from  35?. 

1#&  Required  the  sum  of  24J,  18T53,  and  9|. 

127.  Required  the  difference  between  jf  and  \  J. 

!£?.  Find  the  sum  of  -J,  J,  J,  and  J. 

1#P.  Find  the  difference  between  47?  and  100. 

ISO.  Add  together  % ,  T4T,  and  T52. 

*£/.  Subtract  18 J  from  25  J. 

182.  Required  the  sum  of  \ J,  ^t  and  |J. 

l&S.  From  J  of  T%  take  J  of  /„ . 

1&£.  What  is  the  sum  of  3  J,  T\,  j,  and  jg. 

1#5.  From  19  J  take  §  of  19. 

i3£.  Required  the  amount  of  12|4-42J  +29§. 

187.  Find  the  difference  between  957  and  429^?. 

188.  Add37§  +  43J  +  57i-H;;. 

189.  Subtract  |  of  §  from  §  of  J. 

140.  Required  the  amount  of  }§,  fa,  T75,  and  l. 
Ul.  Subtract  £  of  72  from  100. 


CHAP.   II.]  ARITHMETICAL   EXAMPLES.  35 

142.  What  is  the  product  of  |J  multiplied  by  {%  ? 

US.  How  much  is  19f  times  67T%  ? 

I44.  Multiplicand  57,  multiplier  -fa ;  what  is  the  product  ? 

Ufi.  Multiply  |  of  |  by  -,%  of  |. 

X£0.  Multiply  17|  Plus  13l  ty  I  of  2?- 

147.  What  is  the  product  of  872$  multiplied  by  T93  ? 

148.  Multiplicand  f  f ,  multiplier  \%  ;    what  is  the  product  ? 

149.  Ninety-seven  times  175|  are  how  many  ? 

150.  How  many  are  74T9T  multiplied  by  23 1  ? 

151.  What  is  the  product  of  /T  of  f  multiplied  by  12 \  ? 

152.  Multiply  27-13|  by  11|  plus  12J. 

jT5&  Multiplicand  19|,  multiplier  }§  ;  required  the  product? 

164.  Multiply  I  of  79T  by  §  of  |. 

i55.  What  is  the  product  of  138{4  multiplied  by  |  ? 

156.  Seventy-eight  times  135  j  J  are  how  many  ? 

157.  Multiplicand  f  J,  multiplier  £| ;  what  is  the  product  ? 

158.  What  is  the  result  of  \  f  multiplied  by  jg  ? 

159.  What  is  the  product  of  29-15-/V  multiplied  by  13f  ? 

160.  Multiply  36-15|  by  67-24J. 

161.  Eighteen  multiplied  by  J  plus  13  f  are  how  many  ? 

162.  How  many  are  642  multiplied  by  jf  ? 

163.  Multiply  I  of  751  by  f  of  845. 

164-  How  many  are  16|  multiplied  by  51|  ? 

165.  Fifty-six  times  19f  plus  25 1  are  how  many  ? 

166.  Multiplicand  f  f,  multiplier  £j  ;  required  the  product. 

167.  What  is  the  product  of  §  of  |  multiplied  by  £§  ? 

168.  What  is  the  product  of  |j  multiplied  by  j  of  -|  ? 

169.  Multiply  7567\  by  f  of  %  of  \. 

170.  How  many  are  81 5  f  multiplied  by  14|  ? 
i7i.  What  is  the  result  of  \ \  multiplied  by  {§  ? 
172.  Multiply  11|4  by  14}§  plus  19Jf. 

i7&  What  is  the  product  of  279  multiplied  by  j%  ? 

174.  Multiply  if  of  |i  by  14  of  § . 

i7&  Multiplicand  312|,  multiplier  T8T ;  what  is  the  product  ? 

i7£.  What  is  the  product  of  15J  multiplied  by  15£  ? 

177.  Seventy-five  multiphed  by  §  of  ||  are  how  many  ? 

17&  Multiply  4  off  by  47-12§. 

179.  What  is  the  product  of  625  multiphed  by  1379T  ? 


36  AEITHMETICAL  EXAMPLES.  [CHAP.  IL 

180.  How  many  times  is  31^\  contained  in  12t67t  ? 

181.  Divide  &  of  j  by  g  of  ft. 

1£#.  What  is  the  quotient  of  T%%  divided  "by  |g. 

188.  Required  the  quotient  of  250  divided  by  T43  of  {§. 

18 Jh  How  many  times  is  7  contained  in  \  §  ? 

1&5.  What  is  the  quotient  of  )§  divided  by  |  of  29  ? 

1££.  How  many  times  is  13^  contained  in  724? 

187.  What  is"the  quotient  of  y7^  divided  by  T80  ? 

188.  Dividend  19£f,  divisor  47T74  ;  what  is  the  quotient  ? 
1£0.  Divide  5|  +  6 J  by  |  of  J. 

100.  How  many  times  is  f  {  contained  in  f  §  ? 

101.  How  many  times  is  8  contained  in  T8d45  ? 

192.  Required  the  quotient  of  42  divided  by  {}. 

193.  Dividend  75£§,  divisor  3^\;  required  the  quotient? 
191f.  How  many  times  J|  contained  in  T§  ? 

195.  What  is  the  quotient  of  140  divided  by  \\  ? 

100.  How  many  times  is  y  contained  in  Jf  ? 

197.  Dividend  §  J,  divisor  140  ;  what  is  the  quotient  ? 

10#.  How  many  times  is  f  §  contained  in  30T7?  ? 

100.  What  is  the  quotient  -f  §  divided  by  30T7?  ? 

#00.  Required  the  quotient  of  §|  divided  by  |f. 

201.  How  many  times  is  -|f  contained  in  f  §  ? 

#0#.  Divide  j  of  i,  by  |  of  TV 

208.  Dividend  274295,  divisor  12 ;  what  is  the  quotient  ? 

204.  What  is  the  quotient  of  12  divided  by  274/5  ? 

205.  How  many  times  is  6^  §  contained  in  l$£j  ? 
#0&  Required  the  quotient  of  523  divided  by  fj. 
207.  What  is  the  quotient  of  ft  divided  by  523  ? 
#0#.  How  many  times  is  27 §  contained  in  44 J  ? 

#00.  Dividend  %  of  |,  divisor  ~  of  \  ;  required  the  quotient  ? 

#10.  Divide  13] +  15|  by  16* - 

211.  How  many  times  is  150  contained  in  ££  ? 

#1#.  How  many  times  is  .',]  contained  m  150  ? 

218.  Divide  25J  +  14J  by  18-2?. 

214.  Dividend  87f,  divisor  12. \  +5§  ;  what  is  the  quotient  ? 

#15.  How  many  times  is  12|  contained  in  $  ? 

#10.  What  is  the  quotient  of  f  £  divided  by  ,J  J  ? 

#17.  Required  the  quotient  of  17| +  27J  divided  by  J  ? 


CHAP.  II.]  ARITHMETICAL  EXAMPLES.  37 

218.  Eeduce  |  to  a  simple  fraction. 

219.  Eeduce  J|  to  a  simple  fraction. 

34 

35 

220.  Eeduce  ^|  to  a  simple  fraction. 

o 
613 

221.  Eeduce  -^  to  a  simple  fraction, 

17? 

l3- 

222.  Eeduce  ^f  to  a  simple  fraction. 

o7 

344 

223.  Eeduce  ^-f  to  a  simple  fraction, 

i_3 
#££.  Eeduce  -f-  to  a  simple  fraction. 

_9_ 

225.  Eeduce  ~±  to  a  simple  fraction. 

8 


Eeduce  y^  to  a  simple  fraction. 
35 
12 

##7.  Eeduce  f§  to  a  simple  fraction. 

32 

15? 
.  Eeduce  — -  to  a  simple  fraction. 

).  Eeduce  —  to  a  simple  fraction. 
9 

4  2 

230.  Eeduce  7-7  to  a  simple  fraction. 

14 3 

231.  Eeduce  —  -  to  a  simple  fraction. 

v 

7 

232.  Eeduce  -|-  to  a  simple  fraction. 

_3 

£&2.  Eeduce  ^  to  a  simple  fraction. 

§ 

123- 
£&£•  Eeduce  — ~  to  a  simple  fraction. 

235.  Eeduce  fg  to  a  simple  fraction. 

75 


ARITHMETICAL   EXAMPLES.  [CHAP.  II. 

What  is  the  value  of  }  J  of  a  ton  ? 
287.  Eeduce  4  w.  6  da.  5  h.  30  min.  to  fraction  of  a  year. 

238.  Reduce  12s.  llfd.  to  the  fraction  of  a  pound. 

239.  What  is  the  value  of  T8f  of  an  acre. 

24.0.  Reduce  3  A.  30  p.  108  in.  to  the  fraction  of  a  sq.  mi 

24.1.  Reduce  5  yd.  2  ft.  8  in.  to  the  fraction  of  a  mile. 
2J$.  What  is  the  value  of  f  of  a  mile  ? 

243.  Reduce  15  cwt.  95  lb.  15  oz.  to  fraction  of  a  ton. 

244.  What  part  of  a  pound  is  9  oz.  15  pwt.  7  gr.  ? 

245.  Reduce  24  gal.  3  qt.  1  pt.  to  the  fraction  of  a  hhd. 

246.  What  is  the  value  of  |  of  a  cord  of  wood  ? 

247.  Reduce  |  of  a  yard  to  lower  denominations. 

248.  7  oz.  6  pwt.  16  gr.  to  the  fraction  of  a  pound. 

249.  Reduce  77  jT  of  a  day  to  the  fraction  of  a  minute. 

250.  What  is  the  value  of  §  of  a  year  ? 

251.  Reduce  236  rd.  1  ft.  1  in.  to  a  fraction  of  a  mile. 

252.  Reduce  3  ft.  11  in.  to  the  fraction  of  a  rod. 

253.  What  part  of  a  year  is  8  m.  3  w.  15  da.  ? 

254.  What  is  the  value  of  f  of  a  square  mile  ? 

255.  What  part  of  a  cwt.  is  71  lb.  14  oz.  ? 

256.  Reduce  TU5ug  of  a  cwt.  to  the  fraction  of  a  pound. 

257.  What  is  the  value  of  jf  of  a  year  ? 

258.  What  part  of  3  years  is  25  da.  7  h.  40  min.  ? 

259.  Reduce  3  pk.  7  qt.  1  pt.  to  the  fraction  of  a  busheL 

260.  What  is  the  value  of  ff  of  a  ton  ? 

261.  Reduce  T^T  of  a  bushel  to  the  fraction  of  a  quart. 
Reduce  15  cwt.  1  qr.  87  lb.  to  the  fraction  of  a  ton. 
Reduce  8  oz.  15  pwt.  20  gr.  to  fraction  of  a  pound. 

264-  What  is  the  value  of  /2  of  a  square  mile  ? 

265.  Reduce  1530  inches  to  the  fraction  of  a  cord. 

266.  What  is  the  value  of  T4T  of  a  year  ? 

267.  What  part  of  5  gallons  is  3  qt  1  pt  3  gi.  ? 

268.  Reduce  12  cwt.  75  lb.  9  oz.  to  the  fractien  of  a  ton. 

269.  Reduce  5  oz.  17  pwt.  13  gr.  to  the  fraction  of  a  pound. 

270.  Reduce  9  oz.  4  dr.  12  gr.  to  the  fraction  of  a  pound. 

271.  What  is  the  value  of  \\  of  a  mile  ? 

272.  What  is  the  value  of  \  \  of  a  square  mile  ? 

273.  What  is  the  value  of  T7T  of  an  acre  ? 


CHAP   II.]  ARITHMETICAL   EXAMPLES.  39 

27 J+.  What  quantity  of  molasses  in  4  casks,  containing  sev- 
erally 55^  gal.,  31|  gal.,  27  f^  gal.,  and  58T3f  gal.  ? 

275.  "What  is  the  cost  of  486  f  bushels  of  corn  at  62  J  cents 
per  bushel  ? 

276.  At  \  J  of  a  dollar  a  yard,  how  many  yards  of  cloth  can 
be  bought  for  9  dollars  ? 

277.  How  many  cords  and  cord  feet  of  wood  can  be  put 
into  a  shed  8  ft.  by  18  ft.  7  in.,  and  10  ft.  5  in.  high  ? 

278.  What  quantity  of  loaf  sugar  must  be  sold  at  $.19T% 
per  lb.,  that  the  price  shall  amount  to  $524  ? 

279.  What  is  the  least  common  multiple  of  42,  9, 14  ? 

280.  What  distance  will  a  car  run  in  9|  hours,  allowing  its 
velocity  to  be  23 1  miles  an  hour  ? 

281.  A  man  divided  $24  among  his  children,  giving  them 
T7n  of  a  dollar  apiece ;  how  many  children  had  he  ? 

282.  What  cubical  quantity  of  earth  must  be  removed  in 
digging  a  pit  13J  ft.  deep,  12  j  ft.  long,  and  9|  ft.  wide  ? 

283.  Eeduce  -fg  of  T\  of  f  I  of  6|  to  a  simple  fraction. 

284.  At  j  of  a  dollar  a  basket,  how  many  baskets  of  peaches 
can  be  bought  for  Hi  dollars  ? 

285.  What  is    the  greatest   common   divisor    of   21,  84, 
and  51  ? 

286.  What  quantity  of  land  in  a  lot,  which  is  65£  rd.  long 
and  47  J  rd.  wide  ? 

287.  If  a  family  use  19|  pounds  of  butter  in  7|  days,  how 
many  pounds  each  day  ? 

288.  If  f  of  a  ton  of  coal  cost  6f  dollars,  what  will  1  ton 
cost  at  the  same  rate  ? 

289.  If  $f-  will  buy  j^  of  a  basket  of  peaches,  what  is  the 
price  of  45|  baskets  ? 

290.  What  is  the  difference  between  12f  +5|  and  9j  +2|  ? 

291.  If  1  yd.  of  ribbon  costs  $|,  how  many  yards  can  be 
bought  for  $25  ? 

292.  How  many  yards  of  cloth  worth  $T\  a  yard  must  be 
given  for  11  lb.  of  wool  worth  $f  a  pound  ? 


40  ARITHMETICAL  EXAMPLES.  [CHAP.  IL 

293.  Multiply  91|  by  T90  of  2J  +  67J-J- 

29Jf.  What  quantity  of  wood  is  there  in  a  pile  14T\  ft.  long, 
3f,  ft.  wide,  and  6&  ft.  high  ? 

#05.  If  5t  bushels  of  potatoes  cost  2§  dollars,  how  much  do 
they  cost  a  bushel  ? 

296.  How  much  land  is  there  in  a  square  lot,  measuring 
|374\  rods  on  every  side  ? 

1  297.  How  many  cords,  and  what  will  be  the  cost,  at  HT%% 
per  cord,  of  wood  in  a  pile  40 J  ft.  long,  6  ft  high,  and  8  ft. 
wide? 

298.  If  |  of  a  bushel  of  oats  feed  a  horse  one  day,  how  long 
will  75T90  bushels  feed  him  ? 

299.  Multiply  eight  hundred  seventy  thousand  six  hundred 
fifty-one,  by  three  hundred  seven  thousand  four. 

800.  If  John  can  walk  21  miles  in  J  of  a  day,  how  far  can 
he  walk  in  1  day  ? 

301.  Keduce  jf,  }§,  and  8|  to  the  least  common  denom.  ? 

302.  What  is  the  dhTerence  between  f  of  69  and  §  of  84  ? 


?.  A  man  had  three  bins  of  grain;  in  the  first  81  \  |,  in 
the  second  117gf,  and  in  the  third  145]-f  ;  how  many  in  all  ? 

30Jf.  What  is  a  pile  of  wood  worth  which  is  112  ft.  long,  4 
ft.  wide,  and  6}  ft.  high,  at  $4 \  a  cord  ? 

805.  If  a  man  travel  J  of  a  mile  in  1  hour,  how  long  will  it 
take  him  to  travel  10  miles  ? 

306.  How  much  will  it  cost  to  pave  a  street  £  mi.  long  and 
2 J  rd.  wide,  at  $12  a  square  rod  ? 

807.  How  many  square  yards  in  a  floor  18J  ft  long  and  15| 
ft.  wide? 

80S.  If  18|  yards  of  cloth  cost  $75,  how  many  yards  can  be 
bought  for  $225  ? 

809.  How  many  yards  of  ribbon  at  $.28 f  per  yard  must  be 
given  for  18  quarts  of  berries  at  35  cents  per  quart? 

810.  Multiply  12 J  by  9|,  and  divide  the  product  by  5|. 

811.  What  is  the  value  of  14j  yd.  of  calico  at  $.12£  per  yd., 
and  6  yd.  of  ribbon  at  48|  cents  a  yard  ? 


OHAP.  II.]  ARITHMETICAL   EXAMPLES.  41 

812.  What  is  the  value  of  a  pile  of  wood  48  ft.  long,  8  J  ft. 
wide,  and  4  ft.  high,  at  $7£  a  cord  ? 

313.  Keduce  f ,  |,  and  f  to  a  common  denominator. 

314.  From  forty  trillions,  160  billions,  42  millions,  16 
thousand,  4  hundred,  take  3  trillions,  63  billions,  41  hun- 
dred. 

315.  A  regiment  lost  244  men  in  battle,  which  was  §  of 
the  regiment;  what  was  the  number  of  men  before  the 
battle  ? 

316.  If  I  of  an  acre  of  land  costs  %6§l,  how  much  will  8| 
acres  cost? 

317.  If  13  §  cords  of  wood  cost  $61  j,  what  is  the  price  per 
cord? 

318.  What  is  the  difference  between  13 +  15 J  and  12f  +  64  ? 

319.  If  T6T  of  a  ton  of  hay  costs  $12  J,  what  will  5f  tons 
cost? 

320.  How  many  pounds  of  coffee  worth  $g  a  pound  must 
be  given  for  12  bushels  of  apples  worth  $|  per  bushel  ? 

821.  If  27  bushels  of  potatoes  cost  $18  §,  how  many  bushels 
can  be  purchased  for  $72*}  ? 

322.  How  many  quarts  of  berries  at  27  cents  a  quart  will 
pay  for  25  §  yards  of  carpeting  at  $1|  per  yard? 

828.  If  57  yards  of  cloth  cost  $197*,  what  will  87§  yards 
cost? 

324.  What  will  45 ,%  dozen  eggs  cost  at  $.22]  per  dozen  ? 

325.  How  many  pairs  of  pants  can  be  made  from  196 }  yd. 
of  cloth,  allowing  2g  yards  per  pair  ? 

326.  How  many  bushels  of  potatoes  worth  57£  cents  a 
bushel  will  pay  for  75  bushels  of  corn  at  $.85 f  a  bushel  ? 

327.  How  many  cubic  feet  in  a  wall  27J  ft.  long,  6|-  ft.  high, 
and  2f  ft.  thick  ? 

328.  At  33  \  cents  a  pound,  how  many  pounds  of  coffee  can 
be  purchased  for  $4.66f  ? 

329.  Prom  one  hundred  millions,  two  hundred  forty-seven 
thousand,  take  one  million  four  hundred  nine. 


42  AKITHMETICAL   EXAMPLES.  [CHAP.  II. 

830.  Find  the  difference  between  4J-  x  7§  and  5T72-r-l|. 

831.  From  16|  yards  of  ribbon  12T25  yards  have  been  cut  off; 
how  many  are  left  ? 

332.  Four  pieces  of  cloth  contain  the  following  number  of 
yards:  15 f,  12|,  162,  and  14^l  ;  how  many  yards  in  all  the 
pieces  ? 

333.  What  is  the  difference  between  §  x  j  and  §  of  4  ? 
Saj.  What  cost  247§  A.  of  land  at  $53f  per  A.  ? 

835.  If  28  J  A.  of  land  cost  $625|,  what  cost  10  A.  ? 

836.  Add  47f,  145 j,  10±f,  125  Jf,  13|,  and  12f. 

837.  Which  is  the  greater,  {£  x  J,  or  \$  +  J ;  and  how 
much? 

<&&?.  What  do  I  receive  per  pound  by  selling  16  j  pounds  of 
tea  for  21£  dollars  ? 

839.  What  cost  22|  bales  of  cotton,  each  weighing  4|  cwt, 
at  $24§  per  cwt.  ? 

3JfO.  A  pole  stands  \  in  the  ground,  J  in  the  water,  and  15 
feet  above  the  water.    What  is  the  length  of  the  pole  ? 

3J/.1.  How  many  pounds  of  maple  sugar  at  17 J  cents  a 
pound  will  pay  for  24f  pounds  of  coffee  at  27 J  cents  a  pound? 

8Jf2.  A  man  owing  $96,  paid  at  one  time  $24/3,  and  at 
another  time  $43 f.    How  much  does  he  still  owe  ? 

3£3.  If  one  yard  of  broadcloth  cost  $4^,  how  many  yards  can 
be  purchased  for  $124;}  ? 

844.  If  one  pound  of  coffee  cost  32 §  cents,  what  must  be 
paid  for  97 J  pounds  ? 

345.  If  35?  tons  of  hay  are  sold  for  $880,  what  will  18?  tons 
cost? 

346.  I  exchanged  15  ^  cords  of  bark  at  $9  J  per  cord,  for 
flour  at  $11|  per  barrel.     How  much  flour  did  I  receive  ': 

347.  Having  paid  out  J  and  ±  of  my  money,  I  had  55  dol- 
lars left.    How  much  had  I  at  first  ? 

348.  A  pole  is  \  in  the  mud  and  j  in  ilie  water,  and  14  feet 
above  the  water.    What  is  its  length  ? 

849.  How  many  acres  in  a  piece  of  land  127  j  rods  long  and 
96|  rods  wide  ? 


CHAP.  II.]  ARITHMETICAL  EXAMPLES.  43 

350.  Multiply  87  ten  thousandths  by  27  hundredths. 

351.  Multiply  462  millionths  by  643  thousandths. 

352.  Multiply  25  hundredths  by  25  hundredths. 

353.  Multiply  643  hundred  thousandths  by  482. 

354.  Multiply  52  and  52  hundredths  by  15  and  9  tenths. 

355.  Multiply  375  thousandths  by  375  thousandths. 

356.  Multiply  fifteen  hundred  by  fifteen  hundredths. 

357.  Multiply  ninety-five  and  72  millionths  by  thirty-seven 

358.  Multiply  455  thousandths  by  eight  and  six-tenths. 

359.  Multiply  62  hundredths  by  62  thousandths. 

360.  Multiply  7854  by  twenty-four  ten  millionths. 

361.  Multiply  69  thousand  and  69  thousandths  by  48. 

362.  Multiply  365  thousandths  by  456  ten  thousandths. 

363.  Multiply  7564  millionths  by  forty-seven  hundredths. 
361^.  Multiply  twenty-four  millions  by  84  millionths. 

365.  Multiply  476.042  by  forty-five  and  eight-tenths. 

366.  Multiply  980  ten  thousandths  by  76. 

367.  Multiply  twenty-seven  and  fifteen  thousandths  by  .018. 

368.  Multiply  507.32  by  315  ten  thousandths. 

369.  Multiply  527  ten  thousandths  by  8  hundredths. 

370.  Multiply  twenty-five  thousandths  by  12  hundredths. 

371.  Multiply  67.035  by  forty-three  ten  thousandths. 

372.  Multiply  87  millionths  by  seventy-five  thousandths. 

373.  Multiply  sixty-seven  hundredths  by  19  hundredths. 
374-  Multiply  340000  by  three  hundred  forty  thousandths. 

375.  Divide  579  by  seventy-five  thousandths. 

376.  Divide  6.9705  by  fifty-four  hundredths. 

377.  Divide  seven  hundred  twenty-eight  by  13  hundredths. 

378.  Divide  one  and  three-tenths  by  137  and  8  tenths. 

379.  Divide  46  and  28  hundredths  by  65  ten  thousandths- 

380.  Divide  33  ten  thousandths  by  64  thousandths. 

381.  Divide  eighteen  by  six-tenths. 

382.  Divide  six-tenths  by  eighteen. 

383.  Divide  forty-five  thousand  by  fifty-four  thousandths. 

384.  Divide  forty-five  thousandths  by  fifty-four  thousand. 
885.  Divide  1754  by  twenty- three  and  five  hundredths. 

386.  Divide  one  hundred  twenty-five  by  425. 

387.  Divide  one  hundred  twenty-five  by  .425. 


44  ARITHMETICAL  EXAMPLES.  [CHAP.    IL 

388.  Divide  twenty-three  and  five  hundredths  by  1754. 

889.  Divide  seven  hundredths  by  twelve  millionths. 

890.  Divide  427348  by  forty-seven  ten  thousandths. 

891.  Divide  four  hundred  ninety  thousand  by  .243. 

892.  Divide  3472  by  87.349. 

893.  Divide  four  hundred  and  ninety  thousand  by  4.98. 

894.  Divide  3472  by  .87349. 

895.  Divide  four  hundred  and  seventy-five  by  54268. 

896.  Divide  twelve  by  eight  thousand  and  forty-nine. 

397.  Divide  1649  by  four  hundred  and  ninety  thousand. 

398.  Divide  forty-seven  by  342  ten  thousandths. 

399.  Divide  342  ten  thousandths  by  forty-seven. 

400.  Divide  175  by  twenty-five  thousandths. 

4-01.  Multiply  .35  by  .43  and  divide  the  product  by  T90. 

402.  Divide  18.05  by  2.4  and  multiply  the  quotient  by  .015. 

403.  Multiply  437  by  nine  hundredths  and  divide  by  .012- 

404.  Divide  .075   by  300  and  divide  quotient  by  .  6. 

405.  Multiply  45.2  by  5  tenths  and  the  product  by  .008. 

406.  Multiply  .12  by  74  and  divide  the  product  by  87. 

407.  Divide  427  by  eighteen  hundredths  and  multiply  by  52. 

408.  Divide  194.8  by  .0033  and  multiply  the  quotient  by  78. 

409.  Divide  427  by  .835  and  multiply  the  quotient  by  T70. 

410.  Multiply  .25  x  .25  and  divide  the  product  by  136. 
41t  4725.68^12.4x7  +  4725=what? 

412.  Multiply  1500  by  15  thousandths  and  add  470.053. 

418.  Divide  1000  by  4  thousandths  and  subtract  .000008. 

414-  Multiply  1000  by  4  thousandths  and  add  2  millionths. 

415.  (52763x5  ten  thousandth s+ 42.324) -r 4  tenths=what? 

416.  Divide  247.6156  by  1433  and  multiply  by  .00. 

417.  Divide  1364.251  by  46.3  and  multiply  by  seven-tenths 

418.  Multiply  19  ten  thousandths  by  425  and  divide  by  .75. 

419.  Multiply  1.70254  by  4  tenths  and  add  25000. 

420.  Divide  4295  by  674295  and  subtract  572  millionths. 

.'  /.  Divide  1258  by  .045  and  subtract  35  tan  thousandths. 
jft&  Multiply  27  millionths  by  .12  and  divide  by  .254. 
4?3.  Divide  427.3  by  .25764  and  add  10000  to  the  quotient 
424-  Divide  twenty-five  by  175  and  multiply  by  .25. 
425.  Divide  475  by  325  ten  thousandths. 


CHAP.  II.]  ARITHMETICAL   EXAMPLES.  45 

J/26.  Keduce  13s.  5d.  3  far.  to  the  decimal  of  a  pound. 

427.  Reduce  8  oz.  2  pwt.  6  gr.  to  the  decimal  of  a  pound. 

428.  What  is  the  value  of  .47524  of  a  cwt.  ? 

429.  Reduce  7  fur.  25  rd.  2  yd.  1  ft,  to  the  decimal  of  a  mile. 

430.  What  is  the  value  of  .4627  of  a  ton  ? 
4-3 1.  Reduce  §  £  to  a  decimal  fraction. 

432.  Reduce  3  R.  24  p.  15  yd.  to  the  decimal  of  an  acre. 

433.  What  is  the  value  of  .8743  of  a  year  ? 
434-  Reduce  4  to  a  decimal  fraction. 

435.  Reduce  .5647  to  a  common  fraction. 

436.  Reduce  .27365  of  a  lb.  Troy  to  lower  denominations. 

437.  What  whole  numbers =.3 9542  of  a  £  ? 

438.  What  decimal  fraction =T4T  ? 

439.  Reduce  .03246  of  a  cord  to  lower  denominations. 
44-0.  What  common  fraction =.526  ? 

441>  What  whole  numbers =.05  72 9  of  a  mile  ? 

442.  Reduce  6  qr.  2  na.  2  in.  to  the  decimal  of  a  yard. 

44S,  What  decimal  fraction —\\  ? 

444-  Reduce  7  cd.  ft.  15  cu.  ft.  427  in.  to  the  decimal  cf  a  cd. 

445.  What  is  the  value  of  .4873  of  a  lb.  Apothecaries'  weight  ? 

446-  Reduce  .1728  to  a  common  fraction. 

447.  Reduce  19s.  lid.  3  far.  to  the  decimal  of  a  £. 

44$-  Reduce  {§  to  a  decimal  fraction. 

449.  Reduce  14  cwt.  2  qr.  16  lb.  12  oz.  to  the  decimal  of  a  T. 

450.  Reduce  .4675  of  a  lb.  Troy  to  whole  numbers. 

451.  Reduce  6  m.  3  w.  4  da.  20  h.  40  m.  to  the  decimal  of  a  yi 

452.  Reduce  |  f  to  a  decimal  fraction. 

453.  Reduce  16  quires  of  paper  to  the  decimal  of  a  ream. 
454-  Reduce  .95  to  a  common  fraction. 

455.  Reduce  47  gal.  3  qt.  1  pt.  to  the  decimal  of  a  hogshead* 

456.  What  is  the  value  of  .9213  of  an  acre  ? 

457.  Reduce  227  rd.  12  ft.  to  the  decimal  of  a  mile. 

458.  Reduce  |f  to  a  decimal  fraction. 

459.  Reduce  18  cwt.  15  lb.  9  oz.  to  the  decimal  of  a  ton. 

460.  What  is  the  value  of  .25342  of  a  £  ? 

461.  Reduce  .5274836  to  a  common  fraction. 

462.  Reduce  }§  to  a  decimal  fraction. 

463.  Reduce  75  rd.  4  yd.  10  in.  to  the  fraction  of  a  mile. 


46  ARITHMETICAL   EXAMPLES.  [CHAP.  IL 

4.64..  If  6£  yards  of  cloth  cost  $15],  what  cost  one  yard  ? 
What  cost  17£  yards? 

465.  Perform  the  above  example  decimally. 

466.  What  cost  46  A.  135  rd.  of  land  at  $56.47  per  acre  ? 

467.  What  cost  45  yd.  2  qr.  1  na.  of  cloth  at  $4.75  per  yd.  ? 

468.  What  is  the  value  of  .7536  cwt.  of  coffee  at  37f  cents 
per  pound  ? 

469.  How  much  wood  in  a  pile  13  f  ft.  long,  3|  ft.  wide,  and 
54  ft.  high  ? 

470.  Perform  the  above  decimally. 

471.  What  will  be  the  cost  of  4  cwt.  15  lb.  sugar  at  $15 
per  cwt.  ? 

472.  What  is  the  value  of  a  field  containing  87  A.  147  rd. 
at  $35  per  acre  ? 

473.  How  many  square  feet  in  the  four  walls  of  a  room 
30.25  ft.  long,  25.5  ft.  wide,  and  18.5  ft.  high  ? 

474-  Perform  the  above  example  by  common  fractions. 

475.  How  many  cubic  feet  in  the  above  room  ? 

476.  How  many  sq.  yd.  of  paper  will  cover  the  walls  of  the 
above  room  ? 

477.  Multiply  seven  thousand  by  seven  thousandths. 

478.  From  one  thousand  and  five  thousandths  subtract 
eight  hundred  and  eight  hundredths. 

479.  What  cost  85f  tons  of  coal  at  $9?  per  ton  ? 

480.  Perform  the  above  example  decimally. 

481.  At  $17,625  a  ton,  how  many  tons  of  hay  can  be  pur- 
chased for  $95  ? 

482.  What  cost  .1257  cwt  of  coffee  at  43  cts.  per  pound  ? 

483.  Bought  16  cwt.  40  lb.  of  coffee  at  $35£  per  cwt.    What 
was  the  cost  ? 

484.  What  is  the  value  of  a  pile  of  wood  18]  ft  long,  4  ft. 
wide,  and  6  ft.  4  in.  high,  at  $5  ~  per  cord  ? 

485.  Perform  the  above  example  by  decimal  fractions. 

486.  What  are  the  contents  of  a  field  143 A  rd.  in  length  and 
24.25  rd.  in  width  ? 


CHAP  II.]  ARITHMETICAL  EXAMPLES.  47 

487.  Multiply  one  hundred    twenty-five  thousandths  by 
ninety-seven  hundredths,  and  prove  the  answer. 

488.  Perform  the  above  by  common  fractions. 

489.  What  is  the  value  of  5  oz.  13  pwt.  16  gr.  of  gold,  at 
$275  a  pound  ? 

490.  From  one  and  one  thousandth  take  two  ten  millionths. 
~^491.  How  many  yards  of  carpeting  .75  yd.  wide  will  cover 

a  floor  15.5  ft.  long  and  14.25  ft.  wide  ? 

492.  Perform  the  above  example  by  common  fractions. 

493.  How  many  coats  can  be  made  from  150  yd.  of  cloth  if 
2.3  yd.  are  required  for  each  coat  ? 

494-  What  cost  18|  cords  of  wood  at  $5f  per  cord  ? 

495.  Perform  the  above  example  decimally. 

496.  What  is  the  value  of  -f  of  a  cwt.  ? 

497.  What  is  the  value  of  .3251  of  a  cwt.  ? 

498.  Multiply  one  hundred  eight  thousand,  and  thirteen 
ten  thousandths  by  one  hundred  eight  thousandths. 

499.  What  is  the  value  of  .46235  of  a  mile  ? 

500.  What  is  the  value  of  T8T  of  a  mile  ? 

501.  If  12|  tons  of  iron  cost  $948.53,  what  will  21|  tons 
cost? 

502.  What  cost  15.375  cords  of  wood  at  $8.25  per  cord  ? 

503.  If  18.375  cords  of  wood  cost  $147,  what  cost  one  cord  ? 

504.  Sold  19fi  bushels  of  apples  for  $19.12.     What  should 
I  receive  for  5T\  bushels  ? 

505.  Divide  8753  by  56.14  and  multiply  the  quotient  by  48. 

506.  What  are  the  contents  of  a  floor  18|  ft.  long  and  16| 
ft.  wide  ? 

507.  Perform  the  above  example  by  decimals. 

508.  Multiply  forty-eight  hundredths  by  64  thousandths. 

509.  Perform  the  above  example  by  common  fractions. 

510.  Divide  seventy-four  hundredths  by  57  thousandths. 

511.  Perform  the  above  example  by  common  fractions. 

512.  Multiply  iff  by  ff. 


48  ARITHMETICAL    EXAMPLES.  [CHAP.   II. 

518.  What  is  the  value  of  26  gal.  3  qt.  1  pt.  of  oil,  at  $1.15 
per  gallon  ? 

51Jf.  What  is  the  value  of  17  cwt.  2  qr.  14  lb.  of  sugar  at 
$15,125  per  cwt.  ? 

515.  What  is  the  difference  between  15-f-.15  and  .15-^-15  ? 

516.  How  much  cotton  at  23 1  cents  per  pound  can  be  pur- 
chased for  1784  f  lb.  of  wool  at  .6G 3  cents  a  pound  ? 

517.  If  I  of  a  pound  of  butter  cost  24  cents,  what  will  67  § 
pounds  cost  ? 

518.  What  is  the  value  of  T2T  of  a  pound  Troy. 

519.  What  is  the  value  of  .82573  of  a  pound  Troy  ? 

520.  Multiply  .19  by  .19  and  divide  the  product  by  24. 

521.  Perform  the  above  example  by  common  fractions. 

522.  Multiply  }  of  §  of  12  by  614. 

523.  What  cost  7280  kegs  of  nails,  each  containing  56  lb., 
at  9g-  cents  per  pound  ? 

521f.  If  12.375  oz.  of  gold  cost  $195,  what  will  be  the  cost 
of  1  oz.  ?    What  will  be  the  cost  of  5  lb.  ? 

525.  If  one  pound  of  coffee  cost  23  cents,  what  will  be  the 
cost  of  .4627  cwt.  ? 

526.  Divide  27  hundredths  by  57  hundred. 

527.  Divide  27  hundred  by  57  hundredths. 

528.  How  much  cloth  at  $4.00  per  yd.  must  be  given  for 
6  cwt.  96  lb.  of  coffee  at  $24  per  cwt.  ? 

529.  How  many  cubic  inches  in  a  block  of  marble  16  ft. 
long,  8  ft.  6  in.  wide,  and  5 J  ft.  thick  ? 

530.  A  man  sold  a  farm  containing  145  A.  and  55  rds.  at 
$37\  per  acre.     What  did  he  receive  ? 

531.  If  27|  oz.  of  wool  make  8|  yd.  of  cloth,  how  much 
cloth  can  be  made  from  1  oz.  of  wool  ? 

582.  How  much  sugar  at  13£  cents  a  pound  must  be  given 
for  18  gal.  1  qt.  1  pt.  of  molasses  at  65  cents  per  gallon  f 

538.  How  many  square  yards  in  the  walls  of  a  room  14.26 
ft.  long,  12  ft.  wide,  and  10.25  ft.  high  ? 
58Jh  How  many  cubic  yards  in  the  above  room  ? 


CHAP.  II.]  ARITHMETICAL   EXAMPLES.  49 

535.  A  farmer  had  \  of  his  sheep  in  one  pasture,  *  in  an- 
other, i  in  another,  and  the  remainder,  26,  in  a  fourth.  How 
many  sheep  had  he  ? 

536.  What  cost  .5231  of  an  acre  of  land  at  $2,455  per  rod  ? 

537.  What  cost  f  of  an  acre  of  land  at  $5.75  per  rod  ? 

538.  Bought  §  of  a  ton  of  coal  for  $11}.  What  was  the 
value  of  I  of  a  ton  at  the  same  rate  ? 

539.  A  piece  of  land  5  rd.  square  is  worth  $100.  What  is 
5  square  rods  of  it  worth  ? 

540.  A  piece  of  cloth  containing  2  square  yards  was  sold  for 
$5.  What  would  be  the  price  of  another  piece  3  yards  square 
at  the  same  rate  ? 

5Jfl.  If  .355  of  a  cord  of  wood  cost  $2.50,  what  is  the  price 
per  cord  ? 

5Jf2.  Bought  3  cwt.  95  lb.  of  sugar  at  $12 3  per  cwt.,  and 
paid  for  it  with  wood  at  $5^-  a  cord.  How  many  cords  did  it 
take  to  pay  for  it  ? 

543.  How  much  would  it  cost  to  carpet  a  floor  18  ft.  6  in. 
long  and  14  ft.  3  in.  wide  at  $1.66§  per  yard  ? 

544-  How  many  apples  at  $1.87A  a  bushel  must  bo  giyen  in 
exchange  for  12|  yd.  of  cloth  at  58J  cts.  per  yard  ? 

5Jf5.  At  £1  6s.  4d.  per  yd.,  what  will  be  the  price  of  9f  yds. 
of  broadcloth  ? 

5Jf6.  How  many  cords  of  wood  in  a  pile  40  ft.  6  in.  long, 
7  ft.  high,  and  4  ft.  3  in.  wide  ? 

5^7.  What  would  5|  bales  of  cotton  cost,  each  bale  weigh- 
ing 5.125  cwt,  at  $15.75  per  cwt.  ? 

54S.  8576-i  is  l  of  what  number  ?    }  j  of  what  number  ? 

549.  463.042  is  |  of  what  number  ?    f -J  of  what  number  ? 

550.  947  is  jf  of  what  number  ?    f  §  of  what  number  ? 

551.  .04763  is  T53  of  what  number  ?     ^\  of  what  number  ? 

552.  Divide  420  by  .25  and  multiply  the  quotient  by  .75. 

553.  Divide  420  by  \  and  multiply  the  quotient  by  f . 

554.  Reduce  }§  of  -,/?  to  a  decimal  fraction. 

555.  Reduce  .25  x  .85  to  a  common  fraction. 

3 


50  ARITHMETICAL  EXAMPLES.  [CHAP.   II. 

556.  How  many  cubic  feet  in  a  room  12.3  long,  10  ft.  G  in. 
wide.,  and  10  ft.  higli  ? 

557.  How  many  square  yards  of  paper  will  cover  the  walk 
of  the  above  room  ? 

558.  750  is  .6  of  what  number  ? 

559.  Add  47  ten  thousandths,  15  hundredths,  8  tenths,  492 
millionths,  130  ten  thousandths,  and  5678  ten  milhonths. 

560.  Gave  $85.50  for  llf  tons  of  coal.  What  should  I  give 
for  21|  tons? 

561.  If  a  piece  of  land  5  rods  square  cost  $02.50,  what  will 
40  square  rods  cost  ? 

562.  What  common  fraction  is  equal  to  .875  ? 

563.  What  decimal  is  equal  to  8%  ? 

56Jf..  If  13|  bushels  of  wheat  cost  $16.50,  what  should  be 
paid  for  18  f  bushels  ? 

565.  Bought  a  box  of  sugar  containing  475  lbs.  for  $30. 
Sold  I  of  it  at  8  cents  per  lb.,  and  the  remainder  at  12£  cents 
per  lb.     How  much  did  I  make  by  the  bargain  ? 

566.  Reduce  .478  of  a  lb.  Troy  to  lower  denominations. 

567.  Reduce  T5o9-  of  a  lb.  Troy  to  lower  denominations. 

568.  240  is  .12  of  what  number  ? 

569.  What  are  the  contents  of  &  pile  of  wood  22  ft.  9  in. 
long,  3  ft.  9  in.  wide,  and  6  ft.  3  in.  high  ? 

570.  Add  75  ten  millionths,  42  ten  thousandths,  .37,  .427, 
57.3004,  and  44  thousandths. 

571.  If  f  of  a  ship  and  cargo  are  valued  at  $7854,  what  is 
T8r  of  it  worth  ? 

572.  If  4.75  yards  of  cloth  cost  $15,625,  what  will  17.375 
yards  cost  ? 

573.  When  £42  15s.  6d.  are  paid  for  §  of  a  bale  of  cloth, 
what  sum  should  be  paid  for  the  remainder  P 

57 U.  What  cost  25  yd.  2  qr.  3  na.  of  cloth  at  $4.25  per  yd.  ? 

575.  If  18]  bushels  of  apples  cost  $35.75,  what  will  15.15 
bushels  cost  ? 


CHAP   II.]  ARITHMETICAL   EXAMPLES.  51 

576.  Bought  a  lot  of  land  7T3r  rods  square  for  $5  per  square 
rod,  and  sold  it  for  5  cts.  per  sq.  ft.     How  much  was  gained  ? 

577.  Reduce  .375  to  a  common  fraction. 

578.  Reduce  1||  to  a  decimal  fraction. 

579.  Add  476  thousandths,  527  niillionths,  45  hundredths, 
8  tenths,  75  ten  thousandths,  and  613  hundred  thousandths. 

454 

580.  Reduce  ^|  to  a  simple  fraction,  then  to  a  decimal. 

581.  Reduce  .5357  to  a  common  fraction. 

582.  What  decimal  part  of  a  mile  is  875  feet  ? 

588.  How  many  bushels  of  wheat  at  $1 J  per  bushel  must  be 
exchanged  for  45  gal.  3  qt.  of  molasses  at  $50  per  hogshead  ? 

584.  If  I  own  T\  of  a  ship  and  sell  |  of  my  share,  what  part 
of  the  ship  do  I  sell  ? 

585.  17i-f-15|x6|=what? 

586.  How  many  suits  of  clothes  can  be  made  from  47  yards 
of  cloth,  allowing  6.75  yards  for  each  suit  ? 

587.  What  decimal  fraction  is  equal  to  T%  ? 

588.  What  common  fraction  is  equal  to  .3125  ? 

589.  If  I  of  4  of  a  ton  of  coal  is  worth  $3f ,  what  is  a  ton 
worth  ? 

590.  Reduce  T5T  of  a  ton  to  lower  denominations. 

591.  Reduce  .1357  of  a  yard  to  lower  denominations. 

592.  A  grocer  bought  8  cwt.  30  lb.  of  sugar  for  $88,  and 
sold  it  for  12  cents  a  pound.  How  much  did  he  gain  by  the 
bargain  ? 

593.  f  of  482^-  are  how  many  times  5A-  ? 

594.  927-T-.45  are  how  many  times  48  ? 

595.  A  school-room  is  30  ft.  square  and  20  ft.  high.  How 
many  square  yards  in  the  walls  ? 

596.  How  many  cubic  feet  in  the  above  room  ? 

597.  Bought  75  yards  of  cloth  at  $3.50  per  yard,  and  sold  f 
of  it  for  $6  per  yard,  and  the  remainder  at  $7  pex  yard.  How 
much  did  I  make  by  the  bargain  ? 


52  AKITHMETICAL  EXAMPLES.  [CHAP.   IL 

598.  If  .875  cd.  of  wood  cost  $5.50,  what  cost  1  cord  ? 

599.  If  }?  of  a  cargo  of  wheat  cost  $12,360,  what  sum  will 
pay  for  the  whole  cargo  ? 

600.  What  is  the  difference  between  .75 -=-75  and  75-^.75  ? 

601.  What  is  the  value  of  /T  of  a  year  ? 

602.  What  is  the  value  of  .897  of  a  year  ? 

603.  If  f  of  12  tons  of  coal  cost  $85,  how  much  will  §  of  30 
tons  cost  ? 

604.  Dividend  472,  divisor  15748,  what  is  the  quotient  ? 

605.  (156x25^-13  — 175)  x2-^.15  =  what  ? 

606.  How  many  yards  of  carpeting  will  cover  a  floor  16  j  ft. 
long  and  14|  ft.  wide  ? 

607.  How  many  yards  of  carpeting  will  cover  a  floor  15.75 
ft.  long  and  14.5  ft.  wide  ? 

608.  Divide  579  by  84764  and  prove  the  answer. 

609.  In  a  school,  \  of  the  pupils  study  grammar,  i  arith- 
metic, I  geography,  and  the  remainder,  39,  write.  How  many 
pupils  in  the  school  ? 

610.  What  cost  18|  cords  of  wood  at  $8,755  per  cord  ? 

611.  What  are  the  contents  of  a  board  24  ft.  6  in.  long  and 
1  ft.  3  in.  wide  ? 

612.  From  4  acres  of  land  I  sold  one  piece  20  rods  square 
and  another  piece  containing  20  square  rods.  How  much 
remained  ? 

613.  Keduce  .75  and  .25  to  common  fractions  and  divide 
the  last  by  the  first  ? 

611/..  How  many  square  rods  in  a  field  215^  rods  long  and 
124J  rods  wide  ? 

615.  How  many  acres  in  a  field  215.125  rods  long  and 
124.75  rods  wide  ? 

616.  Reduce  4  of  a  £  to  lower  denominations. 

617.  Reduce  .4763  of  a  £  to  lower  denominations. 

618.  If  §  of  a  cord  of  wood  cost  $7.50,  what  will  a  cord 
cost? 

619.  If  J  of  a  farm  cost  $5000,  what  will  S  cost  ? 


r-HAP.   II.]  ARITHMETICAL   EXAMPLES.  53 

620.  If  I  of  |  of  a  ship  costs  $12,000,  what  will  f  of  the 
remainder  cost  ? 

621.  Subtract  four  hundred  and  twenty-five  ten-thousandths 
from  ten  thousand,  and  multiply  by  .12. 

622.  If  the  tax  on  $9000  is  $180,  what  will  be  the  tax  on 
one  dollar  ?    What  will  be  the  tax  on  $4725  ? 

628.  A  man  left  §  of  his  estate  to  his  oldest  son,  \  to  his 
youngest  son,  and  the  remainder,  $2400,  to  his  daughter. 
What  was  the  value  of  the  estate  ? 

62Jf.  Find  the  greatest  common  divisor  of  214  and  196. 

625.  Find  the  least  common  multiple  of  9,  18,  27,  and  72. 

626.  Eeduce  /g2g,  j}§*  34o3t?  an^-  %%  ^°  their  lowest  terms. 

627.  Reduce  *Jfi>  *&*,  and  S|f*  to  mixed  numbers. 

628.  Reduce  196|,  475f ,  and  4791-}%  to  improper  fractions. 

629.  Reduce  {,  $,  j,  T%,  J,  Jj,  and  {§  to  decimals. 

&?0.  Reduce  §  of  §  of  4  of  T90  of  76T  to  a  simple  fraction 

631.  Add  T\r  and  T9-,  and  subtract  |  from  this  sum. 

632.  Multiply  j%  by  4,  and  subtract  T25  from  the  product. 

633.  Divide  {§  by  |,  and  multiply  the  quotient  by  }§. 
£&£•  Reduce  f  of  a  pound,  Apothecaries'  weight,  to  lower 

denominations. 

635.  Reduce  .65753  of  a  year  to  lower  denominations. 

636.  Divide  8753  by  5648763  and  prove  the  answer. 

637.  A  person,  after  spending  I  and  -j  of  his  money,  had 
$40  left.     How  much  had  he  at  first  ? 

638.  How  many  cubic  feet  in  a  wall  18|  ft.  long,  2  ft.  6  in. 
thick,  and  4.25  ft.  high  ?     How  many  yards  ? 

639.  Reduce  {§,  |,  T8F,  and  {§  to  decimal  fractions. 

640.  What  is  the  value  of  an  estate  if  -J-  of  f  of  it  is  worth 
$64? 

64-1.  In  a  certain  school  there  are  420  pupils,  and  there  are 
twice  as  many  girls  as  boys.     How  many  are  there  of  each  ? 

61$.  How  many  square  ft.  of  glass  in  4  windows  of  12  panes 
each,  each  pane  being  2  ft.  6  in.  long  and  1  ft  3  in.  wide  ? 


CHAPTER  III.; 

PERCENTAGE,  WITH  PRACTICAL  APPLICATION  TO  INTER 

EST,  DISCOUNT,  STOCKS,  COMMISSION,  &c,  PROPORTION, 

PARTNERSHIP,  SQUARE  AND  CUBE  ROOTS. 

1.  What  is  6  per  ct.  of  $27.50  ?  of  $15.25  ?  of  $38.40  ? 

2.  What  is  3%  of  1200  ?  of  50  ?  of  1600  ?  of  498  ? 

3.  What  is  5  j-  per  ct.  of  90  ?  of  100  ?  of  150  ?  of  1800  ? 
Jh  Find  61%  of  $8.50?  $850,  $12.75,  $1275. 

5.  Find  7T3a  per  ct.  of  $200,  of  $500,  of  $1000. 

6.  What  is  8}  per  ct.  of  490  lb.  ?  of  650  lb.  ?  of  47.25  lb.  ? 

7.  Write  decimally  6$,  15$,  12^,  33|#. 

A  What  is  SU%  of  832  ?  of  1200  ?  of  491.50  ? 

9.  Write  decimally  J#,  2-J&  15}#. 
i0.  Write  decimally  75^,  125J%  £#. 
XI  What  is  b%  of  728  ?  7J#  of  648  ?  8J#  of  $500. 

12.  275  is  5$  of  what  number?  19$  of  what  number? 

13.  60  is  what  %  of  240  ?  of  720  ? 

U.  Write  %  decimally,  8J&  5f  #,  7T3^. 

i£.  What  is  20^  of  $150  ?  of  160  lb.  ?  of  400  bushels? 

16.  90  is  what  $  of  450  ?  of  720  ?  of  585  ? 

i7.  75  is  6%  of  what  number?  %  of  what? 

i£.  Write  12$  decimally,  12J&  15J#. 

10.  50  is  what  #  of  300?  of  200?  of  500?  of  325? 

20.  How  many  bushels  are  42§#  of  800  bushels? 

21.  Find  12$  of  4792  miles,  12£$  of  875  dollars. 
0&  What  per  cent  of  $125  is  $25  ?  $30  ?  $40  ? 

#5.  $40  is  what  per  cent  of  $80?  of  $120?  of  $150? 

24.  Write  decimally  7#,  87&  87^,  8^ 

25.  What  is  18$  of  1500  pounds  ?  of  473  tons  ? 

«ff.  $15  is  6  per  ct.  of  how  many  dollars?  8#?  5$?  10#? 
#7.  What  is  9J#  of  48?  lljjjf  12J#?  27*$? 


CHAP.  III.]  ARITHMETICAL  EXAMPLES.  55 

Required  the 

28.  Amount  of  $712.24  from  March  3,  1868,  to  July  11,  1870. 

29.  Interest  of  $430.87  from  May  4,  1869,  to  April  9,  1872. 

30.  Rate  at  which  $800  will  gain  $40  in  10  months. 

31.  Principal  that  will  gain  $37.50  in  4  years  2  months. 

32.  Amount  of  $2000  from  Feb.  17,  1868,  to  Dec.  30,  1872. 

33.  Time  in  which  $360  will  gain  $75. 

34.  Interest  of  $600.50  from  May  7,  1871,  to  Oct.  9, 1873. 

35.  Amount  of  $397.15  from  March  22,  1870,  to  Jan.  4,  1871. 

36.  Interest  of  $500  from  June  12,  1865,  to  Aug.  14, 1872. 

37.  Rate  at  which  $1500  will  gain  $187.50  in  2  years  1  month. 

38.  Principal  that  will  gain  $384  interest  in  4  yr.  3  mo.  6  d. 

39.  Amount  of  $0.98  from  April  4,  1864,  to  Feb.  10, 1873. 
4.0.  Interest  of  $10.36  from  Aug.  20, 1870,  to  Feb.  1, 1871. 
Jt-1.  Time  in  which  $130  will  gain  $5.20  interest. 

42.  Amount  of  $358  from  March  7,  186y,  to  Nov.  12, 1870. 

43.  Rate  at  which  $1000  will  gain  $150  in  2  years  6  months. 

44.  Interest  of  $965.18  from  Jan.  29,  1868,  to  Sept.  9,  1873. 

45.  Interest  of  $847.15  from  April  23,  1868,  to  Oct.  12,  1874. 

46.  Amount  of  $85.13  from  Sept.  9, 1869,  to  March  27, 1874. 

47.  Principal  that  will  yield  $12.64  in  1  year. 

48.  Interest  of  $987.41  from  Jan.  6, 1869,  to  Nov.  10, 1875. 

49.  Amount  of  $820.13  from  Aug.  12, 1871,  to  Dec.  19, 1873. 

50.  Interest  of  $9812.15  from  Sept.  13,  1870,  to  Aug.  15,  1873. 

51.  Time  in  which  $900  will  gain  $72  interest. 

52.  Amount  of  $5762.64  from  March  10, 1873,  to  Sept.  1, 1873. 

53.  Rate  at  which  $750  will  amount  to  $817.50  in  1  year. 

54.  Interest  of  $84.75  from  April  9, 1870,  to  Jan.  1,  1874. 

55.  Amount  of  $198.76  from  May  15,  1864,  to  Nov.  12,  1870. 

56.  Principal  that  will  gain  $200  in  4  years  6  months. 

57.  Interest  of  $1591.03  from  Feb.  6,  1872,  to  Dec.  10, 1873. 

58.  Rate  at  which  $500  will  gain  $100  in  2  years  6  months, 

59.  Interest  of  $470.87  from  Nov.  17, 1870,  to  Dec.  28,  1873 

60.  Amount  of  $58.40  from  Aug.  19,  1843,  to  March  17, 1871. 

61.  Interest  of  $2.35  from  July  15, 1865,  to  Feb.  13, 1874. 

62.  Amount  of  $0.75  from  June  6,  1860,  to  May  12, 1871. 

63.  Amount  of  £95  15s.  6d.  for  2  years  6  months  12  days. 
Perform  the  above  examples  at  5%,  1%,  8J%,  7T3o#,  12$. 


56  ARITHMETICAL   EXAMPLES.  ]_CIIAP.   in 

64.  A  note  for  $500,  dated  July  4,  1849,  has  the  following 
indorsements:  Sept.  5,  1849,  $97.25.  June  3,  1850,  $14.75. 
Aug.  1,  1850,  $217.     What  is  due  Jan.  1, 1853  ? 

65.  On  a  note  for  $2340.24,  dated  March  9,  1870,  the  fol- 
lowing payments  were  made:  April  4,  1871,  $674.19.  Sept 
12,  1872,  $41.17.  Jan.  10,  1873,  $73.45.  June  25,  1874, 
$1500.    How  much  is  due  Feb.  14, 1875  ? 

66.  A  note  for  $2000,  dated  June  1, 1865,  has  the  following 
indorsements:  Aug.  4,  1865,  $75.  Dec.  15,  1865,  $125.75. 
Feb.  24,  1871,  $250.    What  is  due  April  10, 1871  ? 

67.  A  note  for  $248.47,  dated  Oct.  14, 1860,  was  indorsed  as 
follows:  Eeceived,  Jan.  2,  1865,  $32.62.  Jan.  4,  1866,  $50. 
March  15,  1869,  $60.    What  remains  due  April  10, 1870  ? 

68.  A  note  for  $525  is  dated  July  13, 1869.  Indorsements: 
Aug.  10,  1871,  $50.  Nov.  18, 1872,  $150.  July  13, 1873,  $10. 
Sept.  12, 1873,  $100.  Required  the  balance  due  March  12, 
1874. 

69.  A  note  for  $1000,  dated  March  4, 1866,  has  the  follow- 
ing indorsements:  Dec.  1,  1866,  $75.  Dec.  11,  1868,  $246. 
Jan.  3, 1869,  $150.  May  3,  1869,  $50.  What  was  due  Jan.  3, 
1870? 

70.  On  a  note  for  $752.27,  dated  August  5, 1871,  the  follow- 
ing payments  were  made :  March  10,  1872,  $200.  May  15, 
1873,  $23.40.  Sept.  12, 1873,  $175.60.  Dec.  9,  1874,  $95.30. 
How  much  is  due  June  30,  1875  ? 

71.  A  note  for  $1735  is  dated  Feb.  19,  1870.  Indorse- 
ments :  June  29,  1871,  $1000.  Nov.  14, 1871,  $500.  Nov.  14, 
1872,  $5.67.    What  is  due  Dec.  24, 1872  ? 

72.  A  note  for  $75.87,  dated  Nov.  1, 1868,  was  indorsed  aa 
follows :  Received  April  5,  1869,  $10.  May  20,  1871,  $3.10. 
Sept.  4,  1871,  $5.92,  Jan.  1,  1872,  $40.  Required  the  balamv 
due  Oct.  7,  1872. 

78.  On  a  note  for  $800,  dated  May  17, 1864,  the  following 
payments  were  made  :  Feb.  20, 1867,  $114.32.  Aug.  8, 1867, 
$35.  May  16, 1868,  $425.43.  Oct  4, 1868,  $12.  What  was 
due  Sept  1, 1870  ? 


CHAP.  III.]  ARITHMETICAL   EXAMPLES.  57 

7Jf.  A  note  for  $450.61,  dated  Sept.  9,  1869,  had  the  follow- 
ing indorsements:  May  15,  1870,  $78.28.  August  6,  1871, 
$243.27.    Feb.  9,  1873,  $35.50.    What  was  due  Sept.  4,  1873  ? 

75.  A  note  of  $447.13,  dated  Dec.  25, 1865,  has  the  follow 
ing  indorsements  :  June  14, 1868,  $145.25.  Sept.  1, 1868,  $60 
Required  the  amount  due  April  15,  1869. 

76.  A  note  for  $991,  dated  April  1,  1866,  had  the  following 
indorsements:  Feb.  1,  1867,  $70.  July  4,  1867,  $40.  June 
1, 1870,  $200.     Required  the  amount  due  July  1,  1871. 

77.  A  note  for  $5000  is  dated  Jan.  1,  1867.  Indorsements : 
March  1,  1868,  $900.  Sept.  1,  1868,  $1200.  July  4,  1869, 
$2000.     What  was  due  Jan.  1, 1870  ? 

78.  A  note  for  $1200  is  dated  Dec.  25,  1866.  Indorse- 
ments :  April  10,  1867,  $400.  Sept.  20,  1867,  $10.  Not.  15, 
1867,  $300.  March  1,  1868,  $20.  Aug.  10,  1869,  $150.  Re^ 
quired  the  amount  due  Dec.  25,  1870. 

79.  Portland,  Feb.  13, 1870. 
On  demand  I  promise  to  pay  George  Williams  two  hundred 

dollars,  with  interest,  value  received.  George  Curtis. 

Indorsements :  May  10,  1870,  $12.75.  Aug.  15,  1870,  $9. 
Sept.  18,  1870,  $15.  April  4,  1871,  $100.  What  remains  due 
Jan.  1,  1872  ? 

80.  Boston,  Oct.  7, 1869. 
For  value  received,  we  jointly  and  severally  promise  to  pay 

John  Brown  or  order,  $327  on  demand,  with  interest. 

Henry  Curtis. 

Samuel  Hersey. 
On  this  note  were  the  following  indorsements :  Jan.  9, 1870, 
$10.    June  6,  1870,  $90.    March  4, 1871,  $7.     Sept.  10, 1871, 
$120.    What  remained  due  Feb.  13,  1872  ? 

81.  New  Toek,  Sept.  1, 1868. 
For  value  received,  we  promise  to  pay  James  Smith  or  order, 

on  demand,  $490,  with  interest. 

William  Roberts. 
Charles  Williams. 
Indorsements :  March  1,  1869,  $125.    Nov.  12, 1870,  $25. 
April  16,  1871,  $200.    Dec.  5,  1871,  $50.    What  remained 
due  March  12, 1872  ? 

3* 


58  ARITHMETICAL   EXAMPLES.  [CHAP.   III. 

82.  A  note  of  $700  was  dated  Jan.  1, 1865.  Indorsed  July 
1,  1865,  $200.  Jan.  1,  1866,  $300.  What  was  due  July  1, 
1866? 

88.  A  note  for  $500  was  dated  Jan.  1, 1865.  Indorsements : 
March  10,  1866,  $20.  Aug.  1,  1866,  $135.59.  Dec.  12, 1866, 
$20.  May  5, 1867,  $200.  What  was  the  balance  due  July  8, 
1868? 

84.  A  note  for  $850  was  dated  May  1,  1870,  and  indorsed : 
June  1, 1871,  $150.  Sept.  15,  1871,  $12.  Jan.  1,  1872,  $215. 
July  16,  1872,  $10.  Nov.  1,  1872,  $125.  What  remained  due 
Sept.  1,  1873  ? 

85.  A  note  for  $2400  was  dated  Oct.  1,  1870.  Indorsed 
April  1,  1871,  $200.  Dec.  16,  1871,  $300.  April  1,  1872, 
$900.    Kequired  the  amount  due  July  21,  1873. 

86.  A  note  for  $600  was  dated  March  1,  1865.  Indorsed 
May  1,  1866,  $200.  June  16,  1867,  $80.  March  1,  1869, 
$127.    Kequired  the  amount  due  Oct.  16,  1870. 

87.  A  note  for  $287  was  dated  Jan.  1,  1870.  Indorsed  May 
1,1870,  $20.  Feb.  10, 1871,  $15.  Sept.  30,  1871,  $30.  What 
was  the  balance  due  Dec.  31,  1871  ? 

88.  A  note  for  $1000  was  dated  May  1,  1871.  Indorsed 
Oct.  30,  1871,  $75.  July  10, 1872,  $25.  Dec.  19, 1872,  $250. 
Required  the  balance  due  May  1,  1873. 

89.  A  note  for  $240.48  was  dated  July  8, 1868.  Indorsed 
Nov.  17,  1868,  $35.79.  April  20,  1869,  $40.  Nov.  10, 1869, 
$36.75.  Feb.  12,  1870,  $18.25.  What  was  the  amount  due 
April  1,  1870  ? 

90.  A  note  for  $157.87  was  dated  May  1,  1869.  Indorsed 
Dec.  10,  1869,  $10.30.  Nov.  10, 1870,  $15.25.  July  1,  1871, 
$45.    What  was  the  balance  due  Sept  30,  1871  ? 

91.  A  note  for  $3800  was  dated  May  8,  1871.  Indorsed 
Dec.  1,  1871,  $120.  March  6,  1872,  $500.  Nov.  19,  1872, 
#75.    Kequired  the  balance  due  Dec.  30,  1872. 

92.  A  note  for  $520.50,  dated  Sept  12, 1869,  had  the  fol- 
lowing indorsements :  May  5, 1870,  $18.  Sept  20, 1870,  $300. 
What  was  due  August  9, 1871  ? 


CHA?.   III.]  ARITHMETICAL   EXAMPLES.  59 

Required  the 

93.  Present  worth  of  $1200,  due  in  4  years  6  months. 
9Jf.  Discount  of  $600,  due  in  2  years  4  months,  at  8%. 

95.  Bank  discount  of  a  note  for  $350,  due  in  9  months. 

96.  Avails  of  a  note  for  $500,  due  in  3  months,  discounted 
at  a  bank,  the  rate  of  discount  being  7$. 

97.  Present  worth  of  $75.50,  due  in  1  year  8  months. 

98.  Amount  for  which  a  note,  due  in  4  months,  must  be 
given,  that  the  avails  may  be  $500. 

99.  Discount  of  $90.12,  due  in  1  year  9  months,  at  8\%. 

100.  Present  worth  of  $390,  due  in  3  years  8  months. 

101.  Avails  of  a  note  for  $450,  due  in  6  months,  discounted 
at  a  bank,  the  rate  of  discount  being  8%. 

102.  Bank  discount  of  $250  for  4  months  15  days,  at  9%. 

103.  Discount  of  $7G.15  for  2  years  3  months  15  days. 

lOlf.  Amount  for  which  a  note,  due  in  90  days,  must  be 
given,  that  the  proceeds  may  be  $375.25. 

105.  Present  worth  of  $515.40  for  2  years  20  days. 

106.  Bank  discount  of  $120.50  for  5  months  15  days,  at  1%. 

107.  Avails  of  a  note  for  $540,  due  in  2  months,  discounted 
at  a  bank,  at  §%. 

108.  Discount  of  $492.12  for  4  years  G  months  10  days. 

109.  Present  worth  of  $800,  due  in  3  years  25  days,  at  8%. 

110.  Discount  of  $578.25,  due  in  1  month  15  days. 

111.  Bank  discount  of  a  note  for  $400,  due  in  8  months. 

112.  Avails  of  a  note  for  $175,  due  in  4  months,  discounted 
at  a  bank,  the  rate  of  discount  being  9%. 

113.  Bank  discount  of  a  note  for  $1275  for  6  mos.  20  days. 
111/..  Amount  for  which  a  note,  due  in  120  days,  must  be 

raven,  that  the  proceeds  may  be  $7500. 

115.  Present  worth  of  a  note  for  $1800,  due  in  2  yrs.  11  mos. 

116.  Bank  discount  for  $10  for  5  months  1  day,  at  10$. 

117.  Proceeds  of  a  note  for  $629,  due  in  3  months,  dis- 
counted at  a  bank,  the  rate  being  8%. 

118.  Present  value  of  a  note  for  $200,  due  in  28  days. 


60  ARITHMETICAL   EXAMPLES.  [CHAP.  IIL 

119.  What  are  the  net  proceeds  from  the  sale  of  3745  bar- 
rels of  flour  at  $10.50  per  barrel,  commission  being  Z\%  ? 

120.  A  factor  received  $2460.76  for  the  purchase  of  flour 
after  deducting  his  commission  of  %\%.  What  will  be  the 
amount  invested  ? 

121.  What  sum  shall  I  receive  for  negotiating  a  loan  of 
7500,  at  \%  commission  ? 

122.  An  agent  collects  for  a  society  278  bills  of  $7.63  each. 
How  much  must  he  pay  over  if  he  receives  4$  for  collecting  ? 

123.  What  is  the  value  of  27  shares  of  bank  stock  at  a  dis- 
count of  1%\%,  par  value  being  $100  per  share  ? 

124.  What  are  the  net  proceeds  from  the  sale  of  525  bales 
of  cotton  at  $120  per  bale,  after  deducting  %\%  commission  ? 

125.  A  broker  receives  $1752.44  to  invest  in  real  estate, 
after  deducting  his  commission  of  1\%.  What  will  be  the 
amount  invested  ? 

126.  What  are  the  net  proceeds  of  a  consignment,  sold  for 
$2850,  on  which  there  are  charges  of  $235  cartage,  $250  stor- 
age, and  3\%  commission  ? 

127.  Sold  426  bales  of  cotton,  weighing  408  pounds  each,  at 
26  cents  a  pound.    What  is  the  commission  at  2| %  ? 

128.  A  broker  receives  $2195.50  to  invest  in  U.  S.  bonds, 
after  deducting  his  commission  of  \%.  What  will  be  the 
amount  invested  ? 

129.  Sold  my  house  for  $5500.  What  sum  shall  I  receive 
from  the  broker  if  I  pay  him  %\%  for  selling  ? 

130.  How  many  barrels  of  flour  at  $10.25  each  can  a  factor 
purchase  with  a  remittance  of  $2375.90,  after  deducting  %\% 
commission  ? 

131.  What  is  the  value  of  a  draft  on  New  York  for  $1532.45, 
at  1%  discount  ? 

132.  What  is  the  commission  for  selling  goods  amount  in  g 
to  $1758.34,  at  2J#? 

133.  An  agent  received  $14635.70  to  expend  for  cotton,  de- 
ducting his  commission  at  2 \%.  What  value  of  cotton  can  he 
purchase  ? 


CHAP.  III.]  ARITHMETICAL  EXAMPLES.  61 

I84.  How  much  stock,  at  6J%  discount,  can  be  bought  for 
$9650.53  ? 

135.  How  much  money,  at  5%  discount,  will  pay  a  note  for 
$1850  ? 

136.  "What  will  be  the  amount  of  a  bill  of  goods  to  be  pur- 
chased with  the  balance  of  $7548.15,  after  deducting  Z%  com- 
mission ? 

137.  An  agent  purchased  wheat  for  a  flouring  mill  amount- 
ing to  $5247.44.    What  was  his  commission  at  %\%  ? 

138.  An  agent  receives  $1500  for  the  purchase  of  wheat, 
after  deducting  %%%  commission.  What  will  be  the  amount  of 
his  commission  ? 

139.  A  merchant  paid  a  broker  $2600  for  a  quantity  of 
wheat,  and  his  commission  at  3%.  What  did  he  pay  for  the 
wheat  alone  ? 

lift.  What  is  a  draft  for  1728.50  worth  at  %%  premium  ? 

llf.1.  What  is  the  commission,  at  2%,  for  the  purchase  of 
1195  pounds  of  wool  at  34  cents  a  pound  ? 

11$.  If  the  interest  on  a  note  at  7\%  is  $348.72,  what  would 
it  be  at  8f$? 

143.  How  many  yards  of  cloth  can  be  bought  for  $5 82. lb', 
if  174  yards  cost  $695.53  ? 

144.  If  1085  bushels  of  corn  will  grow  on  32  acres  of  land, 
how  much  can  be  produced  on  124  acres  ? 

14.5.  If  a  ship  sail  2694  miles  in  28  days,  how  far  will  she 
sail  in  7  weeks  ? 

14.6.  If  $1200  will  support  a  garrison  45  days,  how  long  will 
$855.42  support  it  ? 

147.  If  a  pasture  will  feed  125  horses  87  days,  how  many 
horses  will  it  feed  58  days  ? 

148.  How  many  pounds  of  sugar  can  be  purchased  for 
.11750,  if  247  pounds  cost  $38.50  ? 

149.  If  a  quantity  of  provisions  will  last  a  regiment  of  965 
soldiers  47  days,  how  many  men  will  it  feed  38  days  ? 

150.  How  many  yards  of  cambric  g  yard  wide,  will  it  take 
to  line  127  yards  of  cloth  If  yards  wide  ? 


62  ARITHMETICAL  EXAMPLES.  [CHAP.   II L 

151.  If  160  pounds  of  tea  cost  $155,  how  much  can  be  pur- 
chased for  $243.12  ? 

152.  What  cost  250  tons  of  coal,  if  32  tons  cost  $297.50  ? 

153.  If  2850  bushels  of  wheat  make  570  barrels  of  flour, 
how  many  barrels  of  flour  can  be  made  from  983  bushels  o* 
wheat  ? 

15 J+.  If  a  man  can  earn  $1200  in  304  days,  how  much  will 
he  earn  in  448  days  ? 

155.  If  an  engine  run  1750  miles  in  85  hours,  how  far  will 
it  run  in  53  hours  ? 

156.  How  many  gallons  of  molasses  can  be  purchased  for 
$1350.40,  if  10  hhds.,  each  containing  124  gals.,  cost  $875  ? 

157.  If  68  men  cut  411  cords  of  wood,  how  many  will  b* 
required  to  cut  1430  cords  ? 

158.  How  many  acres  of  land  can  be  purchased  for  $1500, 
if  824  acres  cost  $12360  ? 

159.  If  450  bushels  of  oats  will  last  40  horses  75  days,  how 
many  days  will  2000  bushels  last  them  ? 

160.  If  20  men  perform  a  piece  of  work  in  35  days,  how 
many  men  will  be  required  to  perform  the  same  in  52  days  ? 

161.  If  5  cwt.  45  lbs.  of  sugar  cost  $82.50,  how  much  sugar 
can  be  purchased  for  $195.40  ? 

162.  If  the  freight  of  118  tons  is  $340,  what  would  be  the 
freight  of  49  tons  3  cwt.  for  the  same  distance  ? 

163.  If  240  men  can  build  a  wall  in  47  days,  how  many 
men  would  build  it  in  68  days  ? 

16 It..  If  a  family  of  9  persons  spend  $1100  in  a  year,  how 
many  dollars  will  be  required  for  a  family  of  7  persons  ? 

165.  If  18  tons  of  coal  cost  $216,  how  many  tons  may  be 
bought  for  $180  ? 

166.  What  cost  93  cords  of  wood,  if  57  cords  cost  $600  ? 

167.  If  |  of  an  acre  of  land  is  worth  $42.50,  what  is  t  lie 
value  of  24 1  acres  at  the  same  price  ? 

168.  If  a  man  perform  a  journey  in  45  days  whin  the  days 
are  12  hours  long,  in  how  many  days  of  14  hours  each  will  he 
perform  the  same  ? 


CHAP.   III.]  ARITHMETICAL   EXAMPLES.  63 

169.  Cost,  $150 ;  profit,  15$.    What  is  the  selling  price  ? 

170.  Selling  price,  $125  ;  loss,  20$.    What  is  the  cost  ? 

171.  Profit,  $30 ;  cost,  $128.50.     Eequired  the  gain  $. 

172.  Loss,  10$ ;  cost,  $12.50.     Eequired  the  selling  price. 

173.  Selling  price,  $125.50 ;  loss,  20$.     Eequired  the  cost. 
17 lh  Cost,  $12  ;  selling  price,  $16.    Eequired  the  gain  $. 

175.  Profit,  25$ ;  cost,  $5.50.    Eequired  the  selling  price, 

176.  Selling  price,  $65.50 ;  profit,  12$.    What  is  the  cost  ? 

177.  Loss,  12^$ ;  cost,  $59.    What  is  the  selling  price  ? 

178.  Cost,  $7.50 ;  profit,  18$.    Eequired  the  selling  price. 

179.  Cost,  $175.20 ;  selling  price,  $200.    Eequired  the  gain  % 

180.  Selling  price,  $280.30  ;  cost,  $300.    What  is  the  loss  $? 

181.  Cost,  $1500  ;  gain,  16|$.     Eequired  the  selling  price. 

182.  Selling  price,  $18.50 ;  loss,  6J-$.    Eequired  the  cost.  ' 

183.  Cost,  $4.50  ;  selling  price,  $6.    What  is  the  gain  $  ? 
181/..  Profit,  $35  ;  cost,  $80.     Eequired  the  gain  $. 

185.  Cost,  $95  ;  profit,  124$.    What  is  the  selling  price  ? 

186.  Loss,  $25.50  ;  cost,  $175.     Eequired  the  loss  $. 

187.  Selling  price,  $125.50  ;  profit,  8 \%.    What  is  the  cost  t 

188.  Selling  price,  $1875  ;  loss,  15$.     What  is  the  cost  ? 

189.  Cost,  $88.60  ;  loss,  7£$.     What  is  the  selling  price  ? 

190.  Profit,  $15  ;  cost  $160.    Eequired  the  gain  $. 

191.  Selling  price,  $75.25  ;  cost,  $50.    What  is  the  gain  $  ? 

192.  Loss  25$ ;  selling  price,  $90.     Eequired  the  cost. 

193.  Cost,  $5  ;  selling  price,  $7.50.    What  is  the  gain  $? 
191^.  Profit,  $12$ ;  selling  price,  $45.    What  is  the  cost  ? 

195.  Selling  price,  $500 ;  gain,  33|$.     What  is  the  cost? 

196.  Cost,  $13.50 ;  selling  price,  $10.    Eequired  the  loss  $? 

197.  Profit,  6]$;  cost,  10  cts.     What  is  the  selling  price? 

198.  Selling  price,  $250  ;  cost,  $190.    Eequired  the  gain  $. 

199.  Cost,  10  cts. ;  selling  price,  12  cts.    Eequired  the  gain  $. 

200.  Profit,  $35  ;  selling  price,  $95.     Eequired  the  gain  $. 

201.  Selling  price,  12  cts. ;  cost,  15  cts.    Eequired  the  loss  $ 

202.  Profit,  $42 ;  selling  price,  $65.    Eequired  the  gain  $. 
90S.  Cost,  $45.20  ;  gain,  13$.    Eequired  the  selling  price. 

204.  Loss,  15$ ;  cost,  $30.     What  is  the  selling  price  ? 

205.  Selling  price,  $1100  ;  gain.  14$.     Eequired  the  cost 

206.  Cost,  $90 ;  gain,  12$.     Eequired  the  selling  price. 


04  AEITHMETICAL   EXAMPLES.  [CHAP.   IIL 

207.  A  merchant  having  $2756  in  the  Canal  Bank  wishes 
to  withdraw  15$.    How  much  will  remain  ? 

208.  What  is  the  amount  of  $450.75  for  4  years  7  months 
15  days,  at  9$. 

209.  If  |  of  a  ship  is  valued  at  $5500,  what  is  %  of  her  worth 
at  the  same  rate  ? 

210.  What  is  the  premium  for  the  insurance  of  a  house 
Valued  at  $6700,  for  1  year,  at  \%  ? 

211.  A  owes  B  $300,  to  be  paid  in  4  months,  $500  in  6 
months,  $200  in  8  months,  and  $400  in  10  months.  Wliat  is 
the  equated  time  for  the  payment  of  the  whole  sum  ? 

212.  If  I  sell  300  bales  of  cotton,  each  weighing  540  pounds, 
at  28  cts.  per  pound,  and  receive  %\%  commission,  how  much 
do  I  make  by  the  transaction  ? 

213.  What  is  the  duty  on  120  hogsheads  of  molasses,  each 
hogshead  gauging  138  gallons,  the  cost  of  the  molasses  being 
38  cts.  per  gallon ;  duty  25%  ? 

2 11^.  What  must  be  paid  for  20  shares  railroad  stock  at  12^ 
advance,  par  value  being  $100  per  share  ? 

215.  How  long  must  $240  be  on  interest  at  8£#  to  gain 
$26.40  ? 

216.  The  avails  of  a  note  having  3  months  to  run,  discounted 
at  a  bank,  were  $1240.95.     What  was  the  face  of  the  note  ? 

217.  If  20  men  build  a  wall  45  ft.  long,  8  ft.  high,  and  4  ft. 
thick,  in  16  days  of  9  hours,  how  many  days  of  8  hours  will 
60  men  require  to  build  a  wall  85  ft  long,  9  ft.  high,  and  3  ft 
thick? 

218.  What  is  the  amount  of  $425.45  for  3  years  6  months, 
at  compound  interest  ? 

219.  A,  B,  and  C  engaged  in  trade.  A  put  in  $400,  B  put 
in  $250,  and  C  put  in  $600.  They  gained  $300.  What  is 
each  man's  share  of  the  gain  ? 

220.  A  horse  which  cost  me  $250  I  sold  for  $300  on  6 
months'  credit.    How  much  did  I  gain  ? 

221.  If  480  bushels  of  oats  will  last  24  horses  18  days,  how 
long  will  640  bushels  last  42  horses  ? 


CHAP.   III.]  ARITHMETICAL  EXAMPLES.  65 

222.  "What  must  be  the  face  of  a  note  at  60  days,  the  pro- 
ceeds of  which,  when  discounted  at  a  bank,  are  $488  ? 

223.  If  $800  gain  $32  in  8  mos.,  what  is  the  rate  of  interest  ? 
22^.  A  town  is  taxed  $12,000  on  its  property  valued  at 

$2,400,000.     What  is  the  tax  on  one  dollar  ? 

225.  What  is  the  duty,  at  20$,  on  240  bales  of  wool,  each 
weighing  400  pounds,  at  28  cts.  per  pound ;  tare  4$  ? 

226.  A  merchant  sold  goods  amounting  to  $480  and  gained 
16 \%.     What  was  the  cost  of  the  goods  ? 

227.  What  is  the  value  of  12  shares  in  the  Merchants'  Bank 
at  12$  premium  ? 

228.  Bought  a  horse  and  carriage  for  $650,  and  sold  them 
for  $800.     What  did  I  gain  per  cent.  ? 

229.  Bought  175  bushels  of  wheat  for  $325,  and  sold  it  for 
$2  per  bushel.     What  per  cent,  was  the  gain  ? 

230.  A  commission  merchant  received  $3312.25  for  the 
purchase  of  goods,  after  deducting  3%  commission.  What 
amount  will  he  invest  ? 

231.  If  I  buy  24  shares  of  bank  stock  at  par  and  sell  it  at 
7^-$  premium,  how  much  do  I  gain  ? 

232.  How  many  500  dollar  U.  S.  bonds  can  be  bought  for 
$6630,  at  10|-$  premium  ? 

233.  How  much  will  eight  500  dollar  7-30  bonds  cost  at 
6J$  premium  ? 

23 Jj..  What  is  the  commercial  discount  on  a  bill  of  goods 
amounting  to  $1250,  sold  on  4  months'  time,  at  5%  off  for 
cash? 

235.  What  is  the  difference  between  four  thousand,  and 
seven  thousandths : 

236.  If  7  cwt.  41  lb.  of  coffee  cost  $247.35,  how  much  can 
be  purchased  for  $324.85  ? 

237.  A  merchant  shipped  a  cargo  amounting  to  $1645,  and 
paid  2|$  for  insurance.     What  was  the  whole  cost  ? 

238.  If  I  pay  $1275  for  an  invoice  of  flour,  for  what  must 
I  sell  it  to  gain  16|$? 


GG  ARITHMETICAL   EXAMPLES.  [CHAP.    IIL 

239,  What  is  the  present  worth  of  a  note  for  $259,  due  in 
1  month,  at  7j-$  bank  discount  ? 

2Jf.O.  Bought  50  bales  of  wool,  each  weighing  380  pounds, 
at  30  cts.  a  pound ;  tare,  h%.  If  I  sell  the  lot  for  $6000,  what 
%  shall  I  gain  ? 

2J/.1.  "When  gold  is  worth  136,  what  is  one  dollar  in  cur- 
rency worth  ? 

2Jfi.  What  is  the  difference  between  the  discount  and  inter- 
est of  $300  for  2  years  6  months,  at  S%  ? 

243.  A  broker  received  $1212  for  the  purchase  of  bank 
stock,  after  deducting  1%  commission.  How  many  $100 
shares  did  he  buy  ? 

244.  A  merchant  having  lost  20$  of  his  capital  had  $2000 
left.     How  much  had  he  at  first  ? 

&£5.  A  man  owes  $2400,  -J  of  which  is  now  due,  J  of  it  in 
3  mo.,  J  of  it  in  4  mo.,  and  the  remainder  in  6  mo.  WTiat  is 
the  equated  time  of  payment  ? 

246.  Divide  four  hundred  and  sixty-eight  millionths  by 
thirteen  thousandths,  and  multiply  the  quotient  by  four  ten- 
thousandths. 

247.  What  would  be  the  duty,  at  25$,  on  75  pieces  of  cloth, 
each  piece  being  32  yards  in  length,  valued  at  23  cts.  per  yd.  ? 

2JfS.  At  $10  a  cord,  what  cost  a  pile  of  wood  18  ft.  6  in. 
long,  4  ft.  3  in.  wide,  and  7  ft,  9  in.  high  ? 

249.  Multiply  twelve-thousandths  by  fifteen  hundred,  and 
divide  the  product  by  five-tenths. 

250.  When  gold  is  135,  what  is  the  value  of  $400  in  cur- 
rency ? 

251.  How  many  cubic  feet  of  wood  in  a  shed  24£  feet  long, 
16J  feet  wide,  and  10}  feet  high  ? 

252.  What  would  be  the  cost  of  the  above  at  $5.50  per  cd.  ? 

253.  Divide  five  thousand  by  five-thousandths,  multiply  the 
quotient  by  six-hundredths,  and  divide  the  product  by  four- 
tenths. 

254.  $400  is  due  June  10,  and  $600  Nov.  10.  When  should 
both  be  paid  ? 


CHAP.   III.]  AKITHMETICAL  EXAMPLES.  67 

255.  Sold  a  quantity  of  goods  for  1351.50,  for  which  I  re- 
ceived a  note  payable  in  six  months.  How  much  did  I  receive 
for  the  goods  ? 

256.  If  two-thirds  of  a  ton  of  coal  cost  $8.33|,  how  much 
will  six-sevenths  of  a  ton  cost  ? 

257.  How  many  cords  of  wood,  at  $5. 12 1  a  cord,  must  a 
man  give  for  9125  bushels  of  wheat  at  11.40  per  bushel,  and 
85  bushels  of  rye  at  $1.25  per  bushel  ? 

258.  Eequired  the  difference  between  the  present  worth  and 
proceeds  of  $600,  due  in  2  years  6  months,  at  6%. 

259.  If  8  yards  of  muslin,  1  j  wide,  cost  $1.25,  what  should 
be  paid  for  10  yards  of  the  same  quality  1-^  yards  wide  ? 

260.  At  what  rate  will  $72.50,  in  3  years  4  months  15  days, 
yield  $1468125  interest? 

261.  A,  B,  and  0,  in  partnership,  gained  $4560.  A's  stock 
was  $4800,  which  was  §  of  B's,  and  B's  was  §  of  O's.  What 
was  the  gain  of  each  ? 

262.  What  is  the  difference  between  the  simple  and  com- 
pound interest  of  $600  for  1  year  6  months  6  days,  at  8%  ? 

263.  The  longitude  of  Philadelphia  is  75°  9'  west,  and  Cin- 
cinnati 84°  24'  west.  Yfhat  is  the  time  at  Cincinnati  when  it 
is  10  A.  M.  at  Philadelphia  ? 

26Jh  What  will  be  the  cost  of  25  loads  of  wood,  each  meas- 
uring 1  cd.,  1  cd.  ft,  12  cu.  ft.,  at  $4.50  per  cord  ? 

265.  Find  the  G.  C.  D.  of  529,  782,  and  1127. 

266.  What  is  the  cost  of  86  yd.  3  qr.  2  na.  of  broadcloth,  at 
$2.7-16  per  yard? 

267.  If  2  tons  12  cwt.  of  coal  cost  $12,875,  what  will  6  tons 
15|  cwt.  cost  ? 

268.  I  bought  150  shares  of  stock  at  97,  and  paid  \%  bro- 
kerage.    How  much  did  I  gain  by  selling  the  same  at  105  ? 

269.  What  is  the  amount  of  $172.43  from  June  23,  1870,  to 
March  4,  1872,  at  7-^? 

270.  When  gold  is  worth  112^,  what  is  the  value  in  gold  of 
$630  in  currency  ? 


68  ARITHMETICAL  EXAMPLES.  [CHAP.   III. 

271.  What  is  the  duty  at  25%  on  50  bags  of  coffee,  each 
containing  124  pounds,  valued  at  38  cents  per  pound  ? 

272.  A  house  valued  at  $5750  is  insured  at  \  of  1%.  What 
is  the  premium  ? 

273.  What  is  the  face  of  a  note  which  yields  $115.80  when 
discounted  at  a  bank  for  90  days  ? 

27 U.  What  amount  of  stock  can  be  bought  for  $7560  and 
allow  \%  brokerage  ? 

275.  If  25^  is  lost  by  selling  flour  at  $9  per  barrel,  what 
was  the  cost  ? 

276.  What  is  the  amount  of  £35  4s.  6d.  for  2  years  and  8 
months,  at  6%  ? 

277.  What  are  the  net  proceeds  from  the  sale  of  320  acres 
of  land,  at  $22.50  per  acre,  commission  for  selling  being  2%  ? 

278.  What  is  the  insurance  on  a  ship  valued  at  $10000,  at 
\%,  including  $1  for  policy  ? 

279.  What  is  the  average  time  for  paying  $50  due  in  30 
days,  $75  due  in  40  days,  $150  due  in  25  days,  and  $100  due 
in  60  days  ? 

230.  A  merchant  bought  9  cwt.  52  lb.  of  coffee  for  $400. 
For  what  must  he  sell  it  per  pound  to  gain  12%  ? 

281.  Supply  the  second  term  in  the  proportion  7 :  ? : :  12 :  36. 

282.  Multiply  thirteen  thousandths  by  sixty-four  hun- 
dredths, and  divide  the  product  by  15. 

283.  Bought  12  boxes  of  shoes,  each  containing  48  pairs,  at 
$.87^  per  pair,  and  sold  the  lot  for  $556.    What  was  the  gam  \  P 

28^.  If  a  piece  of  cloth  300  yards  long  and  1  yard  Avidc 
shrink  5%  in  length  and  3%  in  width,  what  does  it  measure 
after  shrinkage  ? 

285.  In  a  school  of  180  pupils,  6  were  absent.  Required 
the  %  of  attendance. 

286.  If  I  buy  wood  at  $8.24  per  cord  on  6  months'  credit, 
for  what  must  I  sell  it  immediately  to  gain  1 1 

287.  What  is  the  duty,  at  30%,  on  95  boxes  of  tin,  contain- 
ing 115  lbs.  per  box,  invoiced  at  8  cts.  per  pound,  tare  being 
6  pounds  per  box  ? 


CHAP.   III.]  ARITHMETICAL  EXAMPLES.  69 

288.  A  man  has  paid  in  3  years  $685.50  interest,  at  10%. 
What  was  the  principal  ? 

289.  If  75  tons  of  coal  were  required  to  run  5  engines  15 
hours  a  day,  what  number  would  be  required  to  run  30  en- 
gines 12  hours  a  day  ? 

290.  What  is  the  discount  on  $500  due  9  months  hence,  at 
8%? 

291.  A  fox,  200  rods  before  a  dog,  runs  25  rods  in  a  minute ; 
the  dog  follows  at  the  rate  of  40  rods  a  minute.  In  what  time 
will  the  fox  be  overtaken  ? 

292.  A  man  sold  a  chain  for  $224,  and  gained  40%.  What 
did  it  cost  ? 

293.  What  is  the  duty,  at  40%,  on  75  bales  of  wool,  each 
weighing  375  pounds,  invoiced  at  30  cts.  per  pound;  tare, 
10%? 

294..  What  is  the  difference  between  the  discount  and  inter- 
est of  $900  for  3  years  4  months  and  20  days  ? 

295.  Three  men  hired  a  pasture  for  $150.  A  put  in  4 
horses  12  weeks ;  B,  6  horses  10  weeks ;  and  C,  8  horses  15 
weeks.     How  much  must  each  pay  ? 

296.  If  a  quantity  of  provisions  will  last  630  men  108  days, 
how  long  will  the  same  last  210  men  ? 

297.  What  is  the  bank  discount  of  $168.13  for  8  years  5 
months  ? 

298.  What  will  be  the  duty,  at  25%>  on  622  yards  of  linen, 
at  30  cents  per  yard,  and  622  yards  of  cotton  at  17  cents  per 
yard  ? 

299.  A  man  sold  a  watch  for  $95,  which  was  15%  less  than 
cost.     What  did  it  cost  ? 

300.  When  gold  is  quoted  110J,  what  is  the  value  in  cur- 
rency of  $2500^in  gold  ? 

801.  What  is  the  amount  of  $1500  for  1  year  and  4  months, 
at7T30%? 

302.  When  gold  is  quoted  at  111,  what  is  the  value  in  cur- 
rency of  $875  in  gold  ? 

303.  Sold  my  horse  for  $200,  which  was  20%  less  than  his 
value.    What  was  his  value  ? 


70  AKITHMETICAL   EXAMPLES.  [CHAP.   Ill, 

80Jf.  A  merchant  paid  a  broker  $6180  for  a  draft  on  New 
York,  allowing  him  Z%  brokerage  ?  What  was  the  amount 
of  the  draft  ? 

305.  Divide  eight  thousand  by  forty-five  thousandths,  and 
multiply  the  quotient  by  five  ten-thousandths. 

306.  A,  B,  and  0  shipped  coal  from  Philadelphia  to  Port- 
land. A  had  on  board  240  tons,  B  480,  and  C  500  tons.  It 
became  necessary  to  throw  overboard  350  tons.  What  was 
the  loss  of  each  ? 

307.  Find  the  third  term  in  the  following  proportion: 
16  :  80  : :  ?  :  50. 

308.  Bought  20  pairs  of  boots  for  $100,  and  sold  them  at 
$4  per  pair.     What  was  the  loss  %■  ? 

309.  James,  John,  and  Henry  engaged  to  perform  a  piece 
of  work.  James  can  do  it  in  12  days,  John  in  15,  and  Henry 
in  20  days.  In  what  time  can  the  three  together  perform  the 
work  ? 

310.  A  fox  has  60  rods  the  start  of  a  hound,  but  the  hound 
runs  12  rods  while  the  fox  runs  8.  How  many  rods  will  the 
fox  run  before  the  hound  overtakes  him  ? 

811.  Sold  my  horse  for  $100,  and  gained  25^.  What  % 
should  I  have  gained  if  I  had  sold  him  for  $120  ? 

312.  A  note  of  $1600,  payable  in  60  days,  was  discounted 
at  a  bank.     How  much  was  received  for  it  ? 

813.  If  a  man  travels  150  miles  in  5  days,  how  long  will  it 
take  him  to  travel  1200  miles  ? 

314.  A  broker  bought  30  shares  of  bank  stock  at  par  and 
sold  it  at  8 J$  discount.     How  much  did  he  lose  ? 

315.  Kequired  the  amount  of  $860  from  Jan.  25, 1870,  to 
Jan.  5,  1872,  at  9$. 

316.  How  much  will  six  500  dollar  U.  S.  7-30  bonds  cost 
at  8*%  premium  ? 

817.  Required  the  interest  of  three  1000  dollar  U.  S.  bonds 
for  6  months  at  7  ?$%. 

318.  Required  the  amount  of  $24.17  for  11  months  29  days, 
at  9%. 


CHAP.   III.]  ARITHMETICAL   EXAMPLES.  71 

819.  When  4%  is  lost  on  coffee  sold  at  12  cents  per  pound, 
what  was  the  cost  ? 

820.  What  is  the  amount  of  $125  for  2  tyears  6  months,  at 
6%  compound  interest  ? 

321.  A  meiwdant  bought  15  bales  of  calico,  each  containing 
50  pieces  of  30  yards  each,  at  22  cents  per  yard.  For  how 
much  must  he  sell  the  lot  to  gain  16 %%  ? 

322.  What  are  the  avails  of  a  note  for  $1728,  dated  Dec.  29, 
1868,  and  due  April  29,  1869,  discounted  at  the  Casco  Bank  ? 

823.  If  5  barrels  of  flour  serve  a  family  of  12  persons  10 
months,  how  many  barrels  will  serve  a  family  of  8  persons  2 
years  ? 

321f..  A  bankrupt,  whose  property  is  worth  $4000,  owes  A 
$2000,  B  $2500,  and  C  $4500.  To  how  much  is  each  creditor 
entitled  ? 

325.  If  $500  gain  $20  in  8  months,  what  will  $800  gain  in 
6  months  ? 

326.  My  agent  purchased  a  lot  of  land  for  $1432.23,  and  30 
tons  of  hay  at  $12.75  per  ton.  What  will  be  the  amount  of 
his  commission  at  \\%  ? 

327.  My  furniture,  worth  $1800,  is  insured  for  ~  its  value 
at  \%.     What  is  the  premium  ? 

328.  What  is  the  commercial  discount  on  a  bill  of  goods 
amounting  to  $1250,  sold  on  4  months'  time,  at  b%  off  for 
cash  ? 

329.  A  broker  bought  twelve  100  dollar  U.  S.  bonds  at  par 
and  sold  them  at  12]%  premium.     How  much  did  he  gain  ? 

330.  If  12  horses  eat  36  bushels  of  oats  in  9  days,  how  many 
bushels  will  45  horses  eat  in  the  month  of  March  ? 

331.  Multiply  twelve-thousandths  by  fifteen-hundredths, 
and  divide  the  product  by  five-tenths. 

832.  How  many  cubic  feet  of  bark  in  a  shed  42^  feet  long, 
18.5  feet  wide,  and  12]  feet  high  ? 

333.  What  would  be  the  cost  of  the  above  at  $7.50  per  cord  ? 

334.  What  is  the  duty,  at  30%,  on  25  pieces  of  broadcloth, 
eaoh  containing  35  yards,  valued  at  $5.37^  per  yard  ? 


72  ARITHMETICAL   EXAMPLES.  [CHAP.   III. 

335.  Sold  my  horse  for  $200,  which  was  20%  less  than  his 
value.     What  was  his  value  ? 

336.  What  principal  will  gain  $120  in  3  years  4  months  ? 

337.  How  many  square  feet  in  the  four  walls  of  a  room  28 
feet  long,  20  feet  wide,  and  12£  feet  high  ? 

338.  I  wish  to  obtain,  at  a  bank,  $698.25.  For  what  sum 
must  1  give  my  note,  payable  in  4  months  15  days,  at  9%  ? 

339.  A  merchant  sold  flour  at  $12.50  per  ban-el,  and  gained 
12%.  If  ho  sell  at  $13  per  barrel,  what  per  cent,  profit  will 
he  make  ? 

3JfO.  If  two-fifths  of  a  hogshead  of  molasses  is  worth  $36, 
what  is  the  value  of  one-half  of  the  remainder  ? 

3Jfl.  What  is  the  difference  between  the  interest  and  dis- 
count of  $273.50  for  1  year  8  months,  at  8%  ? 

3Jf2.  What  is  the  least  common  multiple  of  24,  13,  8  ? 

SJfi.  If  I  borrow  $5000  in  Portland,  and  lend  it  in  San 
Francisco,  how  much  do  I  gain  in  3  yr.  11  mo.  20  d.  ? 

3JtJf..  A  commission  merchant  received  $12500  to  invest  in 
cotton,  after  deducting  b%  commission.  How  many  bales  of 
400  pounds  each  can  he  purchase  at  35  cents  per  pound  ? 

345.  How  many  square  yards  in  the  Avails  of  a  room  30  feet 
long,  25£  feet  wide,  and  11  feet  high  ? 

346.  A  merchant  bought  9  cwt.  30  lb.  of  coffee  for  $285. 
For  what  must  he  sell  it  per  pound  to  gain  15%  ? 

347.  What  will  be  the  cost  of  seven  hundred  and  fifty 
thousandths  cords  of  wood,  at  $4  per  cord  ? 

3Jf8.  A  man  sent  to  an  agent  $49.75  to  buy  sugar.  What 
must  he  spend,  reserving  2J%  for  commission  ? 

3Jfi.  A  field  40  rd.  long  and  30  rd.  wide  cost  $140.  What 
cost  another  field  75  rd.  long  and  20  ft.  wide  ? 

350.  When  gold  is  quoted  at  112.1,  what  is  the  value  in 
currency  of  $1800  in  gold  ? 

351.  What  is  the  amount  of  $950  for  2  yr.  1  mo.  3  d.,  at 

352.  What  is  the  interest  of  a  1000  dollar  bond  for  G  mo., 
at7T«? 


CHAP.    III.]  ARITHMETICAL  EXAMPLES. 


73 


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383. 
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74  ARITHMETICAL  EXAMPLES.  [CHAP.   IIL 

891.  What  is  the  cube  root  of  12977875  ? 

892.  What  is  the  cube  root  of  444194947  ? 
398.  What  is  the  cube  root  of  99252847  ? 
89  Jh  What  is  the  cube  root  of  67917312  ? 

895.  What  is  the  cube  root  of  157464  ? 

896.  What  is  the  cube  root  of  32461759  ? 

897.  What  is  the  cube  root  of  259694072  ? 

898.  What  is  the  cube  root  of  77308776  ? 

899.  What  is  the  cube  root  of  389017  ? 

400.  What  is  the  cube  root  of  84604519  ? 

401.  What  is  the  cube  root  of  48228544  ? 

402.  What  is  the  cube  root  of  79112000  ? 
408.  What  is  the  cube  root  of  21024576  ? 

404.  What  is  the  cube  root  of  64964808  ? 

405.  What  is  the  cube  root  of  54439939  ? 
40&  What  is  the  cube  root  of  224755712  ? 

407.  What  is  the  cube  root  of  5735339  ? 

408.  What  is  the  cube  root  of  473963  ? 

409.  What  is  the  cube  root  of  5746948  ? 

410.  What  is  the  cube  root  of  21024576  ? 

411.  What  is  the  cube  root  of  178453547  ? 

412.  What  is  the  cube  root  of  264609288  ? 

418.  What  is  the  cube  root  of  12977875  ? 

414.  What  is  the  cube  root  of  247673152  ? 

415.  What  is  the  cube  root  of  1879080904  ? 
410.  What  is  the  cube  root  of  13997521  ? 
417.  What  is  the  cube  root  of  53157376  ? 
Ifl8.  What  is  the  cube  root  of  195112  ? 

419.  What  is  the  cube  root  of  32}  ? 
4^0.  What  is  the  cube  root  of  379  ? 

421.  What  is  the  cube  root  of  160 

422.  What  is  the  cube  root  of  74.088  ? 
428.  What  is  the  cube  root  of  537.24  ? 
424-  What  is  the  cube  root  of  f  g  ? 
i#5.  What  is  the  cube  root  of 

426.  What  is  the  cube  root  of  1576.2364  ? 

427.  What  is  the  cube  root  of  ||{  ? 

428.  What  is  the  cube  root  of  438.643  ? 


CHAP.  III.]  ABITHMETICAL  EXAMPLES.  75 

429.  The  base  of  a  right-angled  triangle  being  60  feet,  the 
perpendicular  90  feet,  what  is  the  hypothenuse  ? 

430.  What  must  be  the  length  of  a  ladder  to  reach  the  top 
of  a  house  24  feet  high,  the  foot  of  the  ladder  being  12  feet 
from  the  house  ? 

4-31.  If  a  line  160  feet  long  will  reach  from  the  top  of  a 
steeple  130  feet  high  to  the  opposite  side  of  the  street,  what  is 
the  width  of  the  street  ? 

482.  If  a  ball  6  inches  in  diameter  weighs  40  pounds,  what 
will  a  ball,  whose  diameter  is  12  inches,  weigh  ? 

433.  If  a  cubical  box  contains  54872  inches,  what  is  the 
length  of  one  of  its  sides  ? 

434-  If  a  triangle,  whose  perpendicular  is  24  feet,  contains 
206  feet,  what  are  the  contents  of  a  similar  triangle  whose 
perpendicular  is  56  feet  ? 

435.  If  the  diameter  of  a  circle  is  20  feet,  what  will  be  the 
diameter  of  another  circle  three  times  the  area  of  the  first  ? 

436.  The  hypothenuse  of  a  right-angled  triangle  being  52 
feet,  the  perpendicular  48,  what  is  the  base  ? 

437.  What  is  the  diagonal  of  a  floor  of  a  room  30  feet  long 
and  24  feet  wide  ? 

438.  If  a  ball  5  inches  in  diameter  weighs  75  pounds,  what 
is  the  weight  of  a  ball  11  inches  in  diameter  ? 

439.  What  must  be  the  length  of  a  ladder  to  reach  to  the 
top  of  a  chimney  50  feet  high,  the  foot  of  the  ladder  being  15 
feet  from  the  chimney  ? 

440.  If  an  ox  that  girts  6  feet  weighs  900,  what  will  be  the 
weight  of  an  ox  that  girts  7  feet  ? 

441*  The  diagonal  of  the  floor  of  a  square  room  is  25  feet. 
What  is  the  length  of  one  side  ? 

442.  If  a  globe,  whose  diameter  is  5  feet,  contains  65.44 
cubic  feet,  what  are  the  contents  of  a  globe  20  feet  in  diam- 
eter? 

443.  The  area  of  a  triangle  is  36  inches,  and  one  side  of  it  is 
9  inches.  What  is  the  corresponding  side  of  a  similar  triangle 
containing  144  inches  ? 


76  ARITHMETICAL   EXAMPLES.  [CHAP.   III. 

444-  If  I  pay  $25  for  the  transportation  of  85  barrels  of 
flour  150  miles,  what  must  I  pay  for  the  transportation  of  350 
barrels  75  miles  ? 

445.  Divide  four  hundred  twenty-seven  by  one  hundred 
fifty-five  millionths,  and  multiply  the  quotient  by  fifteen  ten- 
thousandths. 

446.  If  a  stack  of  hay,  containing  8  cwt.,  is  8  feet  in  height, 
what  will  be  the  height  of  a  similar  stack  containing  3  tons  ? 

447.  What  is  the  surface  of  a  sphere  whose  diameter  is  8000 
miles  ? 

44$-  What  are  the  contents  of  a  sphere  whose  diameter  is 
60  inches  ? 

449.  If  a  pipe  5  inches  in  diameter  will  discharge  a  certain 
quantity  of  water  in  12  hours,  in  what  time  will  a  3-inch  pipe 
discharge  the  same  quantity  ? 

450.  If  a  triangle,  whose  base  is  10  feet,  has  an  area  of  50 
feet,  what  is  the  area  of  a  similar  triangle  whose  base  is  20 
feet? 

451.  If  the  weight  of  a  ball  9  inches  in  diameter  is  40 
pounds,  what  is  the  weight  of  a  similar  ball  12  inches  in 
diameter  ? 

452.  Mr.  A  gives  his  note  to  B  for  $240,  \  payable  in  4 
months,  and  the  other  half  in  8  months.  What  is  the  present 
value  of  said  note,  discount  at  h%  per  annum  ? 

453.  A  merchant  learns  that  his  vessel  and  cargo,  valued  at 
$30000,  have  been  injured  to  the  amount  of  $12000 ;  he  ell' 

an  insurance  on  the  remainder  at  5A$..    What  premium  does 
he  pay  ? 

454.  A  tree  broken  off  20  feet  from  the  ground  and  resting 
on  the  stump,  touches  the  ground  50  feet  from  the  stump. 
What  was  the  height  of  the  tree  ? 

455.  If  18  men  can  build  72  rods  of  wall  in  4  days,  how 
many  rods  will  38  build  in  22  days  ? 

456.  What  number  is  that  which,  being  multiplied  by  fchrei 
thousandths,  the  product  will  be  2637  ? 


CHAP.   III.]  ARITHMETICAL  EXAMPLES.  77 

4-57.  A  can  do  a  piece  of  work  alone  in  10  days,  and  B  in 
13  days.     In  what  time  can  they  do  it  if  they  work  together  ? 

4,58.  If  $120  be  divided  among  three  persons,  A,  B,  and  C, 
so  that  when  A  has  $3,  B  shall  have  $5,  and  0  $7,  how  much 
will  each  receive  ? 

459.  Bought  a  cow  for  $30  cash,  and  sold  her  for  $35  at  a 
credit  of  8  months.  Beckoning  the  interest  at  6^,  how  much 
did  I  gain  ? 

4-60.  How  many  planks  15  feet  long  and  15  inches  wide, 
will  floor  a  barn  which  is  60%  feet  long  and  33J  wide  ? 

461.  A  triangle,  whose  base  is  12  feet,  contains  84  square 
feet.  What  is  the  area  of  a  similar  triangle  whose  base  is  20 
feet? 

4-62.  Four  persons  traded  together  on  a  capital  of  $600,  of 
which  A  put  in  -J,  B  put  in  J,  O  put  in  £,  and  D  the  rest ;  at 
the  end  of  4  years  they  had  gained  $4728.  What  was  each 
one's  share  of  the  gain  ? 

463.  If  50  persons  consume  GOO  bushels  of  wheat  in  3  years, 
how  much  will  278  persons  consume  in  7  years  ? 

464-  If  I  borrow  $2500  in  New  York  and  lend  it  in  Port- 
land, how  much  do  I  lose  in  4  years  and  6  months  ? 

465.  If  a  cable  2  inches  in  diameter  will  sustain  a  weight  of 
8000  pounds,  what  weight  can  be  sustained  by  a  cable  3 
inches  in  diameter  ? 

466.  What  is  the  present  value  of  $2880,  }  payable  in  3 
months,  I  in  6  months,  and  the  rest  in  9  months,  at  Q%  per 
annum  ? 

467.  Bought  cloth  at  $1.25  per  yard,  which,  proving  bad,  I 
wish  to  sell  it  at  a  loss  of  18%.  How  much  must  I  ask  per 
yard  ? 

468.  If  a  ball,  2  inches  in  diameter,  weighs  4  pounds,  what 
will  be  the  weight  of  a  ball  that  is  6  inches  in  diameter  ? 

469.  A  and  B  have  a  joint  stock  of  $2100,  of  which  A  owns 
$1800  and  B  $300  ;  they  gain  in  a  year  $1000.  What  is  each 
one's  share  of  the  profits  ?  • 


78  ARITHMETICAL   EXAMPLES.  [CHAP.   III. 

470.  Sold  cloth  at  $1.25  per  yard  and  lost  15$.  For  what 
should  I  have  sold  it  to  gain  12$  ? 

471.  If  the  freight  of  40  tierces  of  sugar,  each  weighing  34 
cwt.,  150  miles,  cost  $42,  what  must  he  paid  for  the  freight  of 
10  hhds.  of  sugar,  each  weighing  12  cwt.,  50  miles  ? 

472.  I  sold  $6910.80  worth  of  goods  for  a  merchant  at  a 
commission  of  2^$.  How  much  ought  I  to  pay  over  to  my 
principal  ? 

473.  If  a  stack  of  hay,  6  feet  in  height,  weighs  525  pounds, 
what  will  be  the  weight  of  a  similar  stack  that  is  15  feet  in 
height  ? 

474-  If  a  family  of  14  persons  spend  $1120  in  8  months, 
how  much  will  9  of  the  same  family  spend  in  5  months  ? 

475.  A  certain  town  is  to  he  taxed  $4280  ;  the  property  on 
which  the  tax  is  to  be  levied  is  valued  at  $1000000.  Now 
there  are  200  polls,  each  taxed  $1.40.  What  will  be  the  tax 
on  one  dollar  ? 

476.  Suppose  a  cistern  has  two  pipes,  and  that  one  can  fill 
it  in  8A  hours,  the  other  in  4|-  hours.  In  what  time  can  both  fill 
it  together  ? 

477.  A  merchant  has  due  him  $300  to  be  paid  in  60  days, 
$500  to  be  paid  in  120  days,  and  $750  to  be  paid  in  180  days. 
What  is  the  equated  time  for  the  payment  of  the  whole  ? 

478.  Two  men  had  each  $240.  One  of  them  spends  14£ 
and  the  other  18^$.  How  many  dollars  more  did  one  spend 
than  the  other  ? 

479.  If  a  globe  of  2  inches  in  diameter  is  worth  $450,  what 
is  the  value  of  a  globe  4  inches  in  diameter  ? 

480.  The  areas  of  two  similar  triangular  fields  are  80  and 
90  acres,  and  a  side  of  the  former  is  75  rods.  Required  the 
corresponding  side  of  the  latter. 

481.  If  8  barrels  of  flour  will  supply  240  men  for  6  days, 
how  long  will  14  barrels  supply  126  men  ? 

482.  A  merchant  has  due  him  $1500  ;  J  is  to  be  paid  in  2 
months;  \  in  3  months;  and  tlio  ivsl  in  (i  months.  What  is 
the  equated  time  for  the  payment  of  the  whole  ? 


CHAPTER  IY> 

MISCELLANEOUS   EXERCISES   FOR   ADVANCED   CLASSES. 

1.  For  what  sum  must  a  bank  note  be  given  to  obtain,  at 
§%  discount,  $8000  for  6  months  ? 

2.  What  is  the  diameter  of  a  circular  piece  of  land  meas- 
uring 4J  acres  ? 

S.  A  hollow  ball,  10  in.  in  diameter  and  1  in.  thick,  con- 
tains within  itself  another  ball  3  in.  in  diameter.  How  many 
qts.  of  water  will  be  required  to  fill  the  space  between  them  ? 


♦  s'-KMSM'ufr 


3ixi 

5.  On  $860.56,  $149.63  interest  was  paid  for  2  yr.  8  mo. 
3  d.     What  was  the  rate  ? 

6.  What  is  the  outside  length  of  a  cubic  box,  made  of  1  in. 
boards,  that  will  contain  10  bushels  of  grain  ? 

7.  What  will  be  the  cost,  in  Portland,  of  a  bill  of  exchange 
on  London  for  £3000,  the  rate  of  exchange  being  109^  ? 

8.  Add  2i,  3?,!  of  ^,  fofj. 

9.  What  are  the  contents,  in  gallons,  of  a  cask  36  in.  long, 
and  whose  bung  and  head  diameters  are  32  and  26  inches  ? 

10.  I  shipped  to  Boston  850  tons  of  hay,  which  my  agent 
sold  at  $22.50  per  ton.  He  paid  charges  :  For  freight,  $950 ; 
cartage,  $112.50  ;  storage,  $65  ;  and  charged  me  2±%  commis- 
sion on  sales.     What  sum  must  he  remit  to  me  ? 

11.  What  is  the  5th  power  of  the  square  root  of  256  ? 

12.  How  many  posts,  6  feet  apart,  will  be  required  to  build 
8  miles  of  fence  ? 


80  ARITHMETICAL   EXAMPLES.  [CHAP.  IV. 

13.  A  merchant  hires  money  at  a  bank  for  3  mo.,  at  6^, 
with  which  to  pay  his  insurance  premium,  viz. :  On  his  house, 
$4500,  at  \% ;  on  furniture,  $1500,  plate,  $500,  pictures,  $300, 
clothing,  $500,  at  %% ;  on  his  store,  $6000,  at  \% ;  on  stock-in- 
trade,  $20000,  at  1% ;  cost  of  policy,  $1 ;  survey  of  premises, 
$1.50.     For  what  sum  must  the  note  be  given  ? 

U.  Divide  163  by  |  of  44. 

15.  A  man  hires  money  at  6%  with  which  he  purchases 
flour  at  $7.50  per  bbl.  After  keeping  it  60  days,  he  is  obliged 
to  sell  it  at  $7.35  per  bbl.    What  was  the  %  of  his  loss  ? 

16.  Multiply  2i  of  f|  by  If.  of  -y-. 

17.  Find  the  interest,  at  b%,  on  £860  7s.  6d.  for  2  yr.  4  mo. 
15  (L 

18.  A  cubic  foot  of  water  weighs  1000  avoirdupois  ounces, 
and  iron  is  7.8  times  as  heavy  as  water  of  the  same  bulk. 
What  will  be  the  weight  of  a  hollow  iron  ball  15  in.  in  diam- 
eter and  3  in.  thick  ? 

19.  A  note  was  given  on  interest,  at  6$,  Jan.  15,  1869,  for 
$1874.18,  on  which  were  the  following  indorsements :  Dec.  1, 
1869,  $300  ;  March  16,  1870,  $50  ;  Jan.  1,  1871,  $325  ;  Aug. 
13, 1871,  $1200.    What  was  due  Jan.  1,  1872  ? 

20.  Write  out  in  words  and  punctuate  the  following  num- 
ber: 423,486,794,235,376,891,352,698,204,345,789,268,1 73,571,- 
208,999,232,517,303,126,798,321. 

21.  What  is  the  cube  of  93  ? 

22.  A  park,  100  rods  long  and  80  rods  wide,  is  surrounded 
by  a  walk  15  feet  wide.  How  many  cubic  yards  of  gravel  will 
be  required  to  cover  the  walk  5  inches  deep  P 

23.  How  much  water  must  be  mixed  with  45  gals,  of  alco- 
hol, at  $1.65  per  gal.,  to  reduce  the  price  to  $1.35  per  gal.  ? 

24-  A,  B,  and  C  trade  in  partnership.  A  furnishes  ]  the 
capital,  and  is  to  have  j  of  the  gain  for  extra  services.  B  and 
C  furnish  $3000  each,  and  the  gain  is  $5760.  What  is  the 
share  of  each  ? 

25.  What  is  the  difference  between  the  simple,  and  the  com- 
pound interest,  on  $800  for  2  yr.  8  mo.,  at  (J;. 


CHAP.  IV.]  ARITHMETICAL  EXAMPLES.  81 

26.  Subtract  5|  from  9.65,  and  divide  the  difference  by  3 J 
diminished  by  2.65. 

27.  How  many  square  inches  of  gold  leaf  will  be  required 
to  gild  a  ball  13  in.  in  diameter  ? 

28.  If  flour,  sold  at  $12  per  bbl.,  gains  15%,  what  would  be 
the  gain  when  sold  at  $11.25  ? 

29.  A  grindstone,  4  ft.  in  diameter,  has  been  worn  off  4  in. 
all  round.  Allowing  that  the  portion  of  the  stone  within  5  in. 
of  the  centre  is  of  no  value,  what  %  of  the  stone  has  been  used  ? 

30.  In  what  time  will  $475,  at  6%  simple  interest,  amount 
to  $570.95  ? 

31.  Multiply  four  millionths  by  three  and  twenty-seven 
ten-thousandths. 

32.  A  commission  merchant  has  sold  goods  for  me  to  the 
amount  of  $26485,  at  %\%  commission.  What  amount  is  due 
me? 

33.  How  many  men  will  build  60  rods  of  wall  in  10  days, 
if  24  men  can  build  648  rods  in  18  days  ? 

34.  What  is  the  interest  on  $8426.84,  at  7T3^,  for  1  yr.  7 
mo.  8  d.  ? 

35.  A  building  28  ft.  wide,  has  the  gable  ends  15  ft.  high. 
How  long  are  the  rafters  ? 

36.  The  census  of  the  United  States  for  the  several  decades 
from  1790  to  1870,  was  as  follows:  In  1790,  3,929,827;  in 
1800,  5,305,925  ;  in  1810,  7,239,814 ;  in  1820,  9,638,131 ;  in 
1830,  12,866,020  ;  in  1840,  17,069,453  ;  in  1850,  23,191,876 ; 
in  1860,  31,443,322;  in  1870,  38,555,983.  Between  what 
years  was  the  %  of  increase  greatest,  and  what  was  that  %  ? 

37.  Required  the  contents,  and  the  cost  at  $7.50  per  cord, 
of  a  load  of  wood  10  ft.  long,  4  ft.  wide,  and  4  ft.  6  in.  high. 

38.  Coffee  which  cost  24  cents  per  lb.,  was  marked  for  sale 
at  30  cents ;  but  afterwards  was  marked  up  5%,  at  which  price 
200  bags,  averaging  165  lbs.  each,  were  sold.  The  purchaser 
having  failed  before  payment  was  made,  a  compromise  was 
made  at  80  cents  upon  the  dollar.  Did  the  seller  gain  or  lose  ? 
How  much  per  lb.,  and  what  %  ? 

4* 


82  ARITHMETICAL   EXAMPLES.  [CHAP.  IV. 

89.  A  grocer  has  sugars  worth  11,  13,  and  17  cents  per  lb., 
with  which  he  wishes  to  fill  10  bbls.,  of  220  lbs.  each,  so  as  to 
sell  the  mixture  at  15  cents  per  lb.  What  quantity  of  each 
kind  will  he  use  ? 

40.  Keduce.18;  4.17;  .008,3.87;  .42(5  to  common  fractions. 

41.  Subtract  J  of  4  of  2|  from  J  of  §  of  8j ;  reduce  the 
remainder  to  a  decimal,  and  multiply  the  difference  between 
that  decimal  and  3.24  by  6.7. 

42.  Four  notes,  of  $500  each,  are  given  for  3,  6,  9,  and  12 
months  respectively.  In  how  many  months  may  they  all  be 
paid  at  one  time  ? 

43.  A  horse  is  teddered  by  a  rope  45£  ft.  Icng.  What  is 
the  area  of  the  ground  upon  which  he  can  graze  ? 

44-  What  will  be  the  contents,  in  cord  measure,  of  the 
trunk  of  a  tree  65  ft.  long,  and  2J  ft.  in  diameter  at  one  end, 
and  10  in.  at  the  other  ? 

45.  What  will  be  the  amount  of  $160,  at  6%  compound  in- 
terest, payable  quarterly,  from  Sept,  1, 1870,  to  Dec.  13, 1871  ? 

46.  Divide  two  tenths  by  five  ten-millionths. 

47.  A  drover  disposed  of  a  lot  of  cattle,  for  ready  money, 
for  $23750,  and  after  making  purchases,  for  cash,  amounting 
to  $1300,  he  went  to  the  bank  and  took  up  a  note,  on  which 
he  had  previously  received  $8000  for  3  months.  After  re- 
serving $230  for  personal  expenses,  he  made  a  purchase  of 
merchandise  amounting  to  $20000,  for  which  he  paid  the 
remainder  of  his  money,  and  obtained  the  balance  from  the 
bank  for  6  months.    Tor  what  amount  was  his  note  drawn  ? 

48.  How  many  yards  of  carpeting  will  be  required  to  carpet 
a  room  15  ft.  8  in.  by  12  ft.  ? 

49.  When  brooms  are  $3.50  per  dozen,  with  a  discount  of 
h%  on  bills  over  $100,  what  will  be  the  cost  of  1GI  gross  ? 

50.  What  is  35$  of  the  area  of  a  rectangular  piece  of  land 
24  rods  long  and  14J  rods  wide  ? 

51.  If  a  ball  3  in.  in  diameter  weighs  12  lbs.,  what  will  be 
the  weight  of  a  ball,  of  similar  density,  8  in.  in  diameter  ? 


CHAP.    IV.]  AEITHMETICAL  EXAMPLES.  66 

52.  What  are  the  contents  of  a  stock  of  13  boards  16  ft 
long,  15  in.  wide  at  one  end,  and  11  in.  at  the  other  ? 

53.  How  many  bushels  of  wheat  can  be  placed  in  a  car  20 
'ft.  long,  8  ft.  wide,  and  7  ft.  high  ? 

5Jf..  A  person  being  asked  the  time  of  day,  replied  that  it 
was  between  10  o'clock  and  11,  and  that  the  hour  and  the 
minute  hands  were  together.     What  was  the  time  ? 

55.  In  the  corner  of  a  room  is  a  pile  of  grain,  in  quarter 
cone  form,  whose  height  is  5  ft.  and  slant  height  8  ft.  What 
number  of  bushels  does  it  contain  ? 

56.  A  grocer  purchased  13  hhds.  of  molasses  at  70  cts.  per 
gal.,  and  sold  it  so  as  to  gain  on  the  whole  $57.33.  At  what 
price  per  gal.  was  it  sold,  and  what  was  the  gain  %  ? 

57.  Required  the  number  of  square  yards  in  the  ceiling 
and  walls  of  a  room  of  the  following  dimensions :  15  ft.  6  in. 
long,  14  ft.  wide,  and  10  ft.  high.  The  room  contains  4  win- 
dows, each  3  ft.  6  in.  by  5  ft.  8  in. ;  2  doors,  each  6  ft.  4  in. 
by  2  ft.  6  in.;  1  fireplace,  3  ft.  high  and  3  ft.  6  in.  long.  And 
what  will  be  the  cost  of  lathing  and  plastering  the  room,  at 
thirty-seven  and  a  half  cents  per  square  yard  ? 

58.  A  gentleman  has  a  note  in  a  bank,  on  which  he  re- 
ceived $575  for  3  mos.,  at  4$  discount ;  and  in  order  to  take 
up  the  note,  he  goes  to  another  bank  and  obtains  the  money 
for  6  mos.  at  6%.  For  what  amount  was  the  last-named  note 
given  ? 

59.  A  well  was  dug  in  a  circular  form  6  ft.  in  diameter,  and 
was  then  lined  with  a  wall  8  in.  thick.  When  the  water  is  11 
ft.  deep,  what  number  of  hhds.  does  it  contain  ? 

60.  When  exchange  is  at  108,  what  will  be  the  face  of  a  bill 
on  Liverpool  that  can  be  purchased  for  $14400  ? 

61.  If  16  men  can  cut  320  cords  of  wood  in  8  days,  how 
many  cords  can  22  men  cut  in  17  days  ? 

62.  The  value  of  the  real  estate  in  a  town  is  $2,385,000 ; 
personal  property,  $865,000 ;  and  a  poll  tax  of  $2  is  assessed 
upon  935  persons.  The  town  raises  by  taxation :  For  schools, 
$12,000 ;    roads  and  bridges,  $4000 ;    support  of  the  poor, 


84  ARITHMETICAL  EXAMPLES.  [CHAP.   IV. 

$3000 ;  pay  of  town  officers,  $800 ;  interest  on  town  debt, 
6320 ;  fire  department,  $1000 ;  contingent  expenses,  $3500. 
What  will  be  the  tax  on  each  $  of  valuation ;  and  what  will 
be  the  whole  tax  of  A,  whose  property  is  valued  at  $5000,  and 
who  pays,  also,  the  poll  tax  ? 

63.  Reduce  §  of  }§  of  -fa  to  a  decimal. 

$4.  What  will  be  the  cost,  at  70  cts.  per  gal.,  of  a  cask  of 
molasses,  whose  length  is  16  inches,  head  and  bung  diameters, 
10  and  12  inches  ? 

65.  Required  the  average  time  for  the  payment  of  the  fol- 
lowing bills  of  goods  purchased  Jan.  1,  1872 :  $150,  payable 
Jan.  15 ;  $300,  payable  Feb.  10 ;  $600,  payable  March  1 ;  and 
$1000,  payable  April  15. 

66.  Find  the  least  common  multiple  of  8,  14,  16,  21,  33,  77, 
85,  165. 

67.  Had  1  cent  been  placed  at  6%  simple  interest  at  12 
o'clock,  noon,  on  the  day  of  the  Declaration  of  the  Indepen- 
dence of  the  United  States,  what  would  have  been  the  amount 
of  the  investment  at  3  o'clock  P.  M.  Jan.  1,  1872  ? 

68.  At  what  time  between  2  and  3  o'clock  do  the  hour  and 
the  minute  hands  of  the  clock  point  in  opposite  directions  ? 

69.  Divide  \ J  of  ){  of  16  by  g  of  f}. 

70.  Give  the  whole  contents  of  4  loads  of  wood  of  the  fol- 
lowing dimensions :  8  ft.  long,  5  ft.  3  in.  high,  and  4  ft.  wide ; 
12  ft.  long,  4  ft.  high,  and  4  ft.  2  in.  wide ;  9  ft.  long,  3  ft.  4 
in.  high,  and  3  ft.  6  in.  wide ;  16  ft.  long,  3  ft,  high,  and  3  ft 
6  in.  wide. 

71.  How  many  bushels  of  grain  are  there  in  a  conical  pile 
5  ft.  high,  and  26  ft.  in  circumference  ? 

72.  What  is  the  length  of  a  diagonal  path  across  an  acre  of 
and  in  the  form  of  a  square  ? 

73.  Find  the  amounts  for  which  bank  notes  must  be  given, 
respectively,  to  obtain  the  following  sums  for  the  times  spe- 
cified : 

$800    for  3  mos.  $1200  for  2  mos. 

$4000  for  6  mos.  $200    for  4  mos. 


CHAP.  IV.]  ARITHMETICAL   EXAMPLES.  85 

74.  What  is  the  greatest  common  divisor  of  1177,,  1819, 
2782,  4708  ? 

75.  What  is  the  average  time  for  the  payment  of  the  follow- 
ing notes,  without  grace  ?  Jan.  1,  $300  on  4  mos. ;  Feb.  1, 
$600  on  6  mos. ;  March  15,  $800  on  9  mos. 

76.  When  exchange  is  at  108f ,  and  brokerage  at  \%,  what 
will  be  the  cost  of  a  bill  on  Liverpool  for  £400  ? 

77.  How  large  a  stick  of  square  timber  can  be  made  from  a 
log  20  in.  in  diameter  ? 

78.  Eeduce  jf*  to  a  decimal  of  eight  places,  and  extract 
the  square  root  of  the  same. 

79.  A  greyhound  running  91  rods  a  minute  is  f  of  a  mile 
behind  a  fox  running  75  rods  a  minute.  In  how  many 
minutes  will  the  hound  overtake  the  fox,  and  how  far  will 
each  travel  ? 

80.  What  number  is  that  which  being  increased  by  f  of 
itself,  and  then  doubled,  gives  4  more  than  the  square  root  of 
2704? 

81.  What  is  the  diameter  of  a  ball  equal  in  bulk  to  8  balls, 
each  2  in.  in  diameter  ? 

82.  Does  a  man  gain  or  lose,  and  how  much,  who  obtains 
at  a  bank  $1000  for  a  year  at  6f0  discount,  and  then  puts  it  at 
interest  for  the  same  time  and  rate  ? 

88.  What  is  the  present  worth  of  $2500  due  in  9  mos.  ? 
8J/..  How  many  bricks,  4  by  8  in.,  will  pave,  a  walk  10  ft. 
wide  and  4  rods  long  ? 

85.  For  a  pile  of  wood  54  ft.  long,  4  ft.  wide,  and  6  ft.  4  in. 
high,  $80.16  was  paid.  How  many  cords  were  there,  and 
what  was  the  price  per  cord  ? 

86.  If  I  buy  bank  stock  at  17$  above  par,  what  %  do  I  re- 
ceive on  my  investment,  if  the  bank  pays  a  dividend  of  %l% 
:on  par  value  ? 

87.  What  will  it  cost  to  plaster  a  room  15  ft.  6  in.  long,  13 
ft.  8  in.  wide,  and  9  ft.  high,  at  26  cts.  per  square  yard  ? 

88.  The  longitude  of  Portland  is  70°  15',  and  that  of  Chi- 
cago 87°  38'.  What  is  the  difference  of  time  between  the  two 
places  ? 


86  AKITHMETICAL  EXAMPLES.  [CHAP.   IV. 

89.  Estimating  the  weight  of  rails  at  65  lbs.  per  yd.,  what 
is  the  entire  weight  of  the  rails  used  in  constructing  the 
Grand  Trunk  Railway  from  Portland  to  Montreal,  a  distance 
of  297  miles  ? 

90.  A  pond  whose  area  is  1000  acres,  supplies  a  city  of 
250,000  inhabitants  with  water.  Estimating  the  consumption 
of  water,  for  all  purposes,  at  100  gals,  per  day  for  each  person, 
how  much  would  a  week's  use  of  water  lower  the  pond  ? 
And  if  the  tributaries  to  the  pond  carry  into  it,  altogether, 
1,100,000  gals,  per  hour,  what  change  would  be  made  in  the 
depth  of  the  water,  by  the  influx  and  use,  in  a  month  of  30 
days? 

91.  How  many  square-edged  boards  of  equal  width  can  be 
made  from  a  log  18  ft.  long  and  16  in.  in  diameter,  allowing 
\  in.  for  sawcut;  and  what  would  be  the  board  measure  of 
the  whole  ? 

92.  A  jeweler  purchased  a  bar  of  silver  weighing  5 J  lbs. 
Av.  at  $1.10  per  oz.,  and  sold  it  at  the  same  price  per  Troy  oz. 
Did  he  gain  or  lose,  and  how  much  ? 

98.  An  agent  received  $10,200  with  which  to  purchase 
wheat  at  $1.25  per  bushel,  after  deducting  his  own  commis- 
sion of  2%  on  money  paid  out.  How  many  bushels  did  he 
buy? 

9^.  A  merchant,  during  his  first  year  in  business,  increased 
his  capital  by  }  of  itself;  and  the  second  year  by  |  of  itself. 
During  the  third  year  he  lost  f  of  all  he  had,  and  had  remain- 
ing $15,000.     What  was  his  capital  at  first  ? 

95.  Extract  the  square  root  of  11000.00011. 

96.  Find  the  cost  per  yd.  of  a  piece  of  cloth  of  14  yds., 
which  sold  for  $61.25  at  a  gain  of  25^. 

97.  Sold  cloth  at  $2,621  per  yd.  at  a  loss  of  12.J#.  At 
what  price  should  I  have  sold  it  to  gain  the  same  %  ? 

98.  If  a  plough  turns  a  furrow  15  in.  wide,  how  far  will  a 
yoke  of  oxen  travel  in  ploughing  4  acres  of  land,  allowing  that 
for  every  20  rods  ploughed  they  travel  1  rod  in  turning  at  the 
corner  ? 


CHAP.    IV.]  ARITHMETICAL   EXAMPLES.  87 

99.  A  has  5  rolls  of  bread  and  B,  3 ;  C  has  none,  but  joins 
them  in  their  meal,  and  proposes  to  pay  for  the  whole  with  8 
pieces  of  money  of  equal  value.  How  should  the  money  be 
divided  between  A  and  B  ? 

100.  A  gentleman  has  a  garden  of  |  of  an  acre  in  the  form 
of  a  square,  which  he  wishes  to  inclose  with  a  brick  wall  16 
in.  thick  and  9  ft.  high.  Allowing  |  in.  for  each  course  of 
mortar,  how  many  bricks  will  be  required  ? 

101.  The  diameter  of  the  earth  is  (nearly)  8000  miles,  and 
that  of  the  planet  Jupiter  about  88000 ;  but  its  density  is 
only  \  of  that  of  the  earth.  How  many  times  heavier  than 
the  earth  is  Jupiter  ? 

102.  A  man  builds  a  railroad  at  $33000  per  mile.  When 
completed,  he  finds  that  it  has  cost  him  $95  per  rod.  What 
%  does  he  make  on  money  expended,  and  what  is  his  whole 
gain  on  a  section  of  9  miles  ? 

103.  If  30  men  build  a  wall  90  ft.  long,  8  ft.  high,  and  4  ft. 
thick,  in  16  days  of  10  hours,  how  many  days  of  8  hours  will 
60  men  require  to  build  a  wall  120  ft.  long,  10  ft.  high,  and  3 
ft.  thick  ? 

104.  A  coal  dealer  purchases  275  long  tons  (2240  lbs.)  of 
coal  at  $6  per  ton ;  and  after  paying  for  freight,  insurance, 
and  other  charges,  $595,  sold  it  at  $9.50  per  ton  of  2000  lbs. 
What  was  his  whole  gain,  and  what  the  %  ? 

105.  Sold  a  bill  of  merchandise  at  wholesale  at  30$  off,  and 
5%  off  for  cash.    What  was  the  whole  discount  ? 

106.  If  a  laborer  can  remove  1  cubic  yd.  of  earth  per  hour, 
what  will  be  the  expense  of  digging  a  ditch  200  ft.  long,  4  ft. 
wide,  and  3  ft.  deep,  allowing  for  wages  $1.75  per  day  of  10 
hours  ? 

107.  When  gold  is  at  125,  what  is  the  gold  value  of  $1500 
in  currency  ? 

108.  What  is  the  face  of  a  draft  that  can  be  purchased  for 
$2500  when  exchange  is  at  2%%  discount  ? 

109.  What  is  the  length  of  a  rope  extending  from  the  top 
of  a  pole  40  ft.  high  to  the  top  of  a  stake  13  ft.  high  standing 
35  ft.  from  the  pole  ? 


88  ARITHMETICAL   EXAMPLES.  [CHAP.   IV. 

110.  There  are  two  fields,  each  containing  10  acres ;  one  in 
the  form  of  a  square,  and  the  other  4  times  as  long  as  it  is 
wide.  What  will  be  the  difference  in  the  expense  of  fencing 
the  two  fields,  the  cost  of  the  fence  being  $2.25  per  rod  ? 

111.  In  what  time  will  $750  amount  to  $960.85  at  7T30^  ? 

112.  How  much  money  must  be  invested  to  build  a  wall 
worth  $325,  and  to  renew  it  every  15  years,  allowing  6%  com- 
pound interest  ? 

US.  In  a  warehouse  A  has  350  bbls.  flour,  worth  $8.25  per 
bbl. ;  B  has  275  bbls.,  worth  $9 ;  and  C  has  2500  bushels  of 
corn,  worth  $1.10  per  bushel.  The  building  takes  fire,  and 
the  damaged  flour  and  grain  is  sold  all  together  for  $3100. 
How  shall  this  money  be  divided  between  A,  B,  and  C  ;  what 
was  each  man's  actual  loss,  and  his  loss  %  ? 

lilt..  A  began  business  Jan.  1  with  a  capital  of  $2000 ;  May 
1  he  received  B  as  a  partner  with  $1500  ;  and  Sept.  15  C  en- 
tered the  firm  with  $3000.  On  the  first  of  the  following  July 
they  dissolved  partnership  and  found  that  their  profits  were 
$5800.     How  much  belongs  to  each  partner  ? 

115.  Add  all  the  prime  numbers  from  1  to  59  inclusive,  and 
extract  the  square  root  of  the  sum. 

116.  An  estate  of  $19000  is  to  be  divided  between  a  widow, 
three  sons  and  a  daughter,  in  such  a  way  that  each  son  shall 
have  $1000  more  than  the  daughter,  and  the  widow  $1000 
more  than  all  the  children.    What  will  be  the  share  of  each  ? 

117.  A  railroad  company  wish  to  build  a  fence  on  both 
sides  of  a  section  of  their  road  13  miles  in  length.  The  fence 
must  be  5  boards  high,  each  8  in.  wide,  and  the  posts  are  to 
be  placed  8  feet  apart.  There  is  also  to  be  nailed  upon  each 
post,  over  the  boards,  a  cleat  4£  ft.  long  and  6  in.  wide.  The 
cost  of  the  boards  is  $13  per  M.,  and  of  the  posts  35  cts.  each. 
What  will  be  the  total  cost  of  the  lumber  ? 

118.  Divide  42  ft.  2'  8"  by  3  ft.  4'. 

119.  Assuming  the  weight  of  iron  as  in  Example  18,  what 
will  be  the  weight  of  112  miles  of  telegraphic  wire  £  in.  in 
diameter? 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  89 

120.  One  man  travels  north  3  days,  at  the  rate  of  175  miles 
per  day ;  and  another  travels  west  the  same  time  at  the  rate 
of  150  miles  per  day.     How  far  apart  are  they  ? 

121.  There  are  two  persons  of  the  same  ages ;  bnt  if  one 
was  10  years  older,  and  the  other  6  years  younger,  the  former 
would  he  twice  as  old  as  the  latter.    What  is  their  age  ? 

122.  How  many  square  feet  of  glass  are  there  in  8  windows 
of  12  panes  each,  the  size  of  the  panes  being  10'  by  14'  ? 

123.  Find  the  greatest  common  divisor  of  624,  480,  and 
1008. 

124..  What  will  be  the  length  of  one  side  of  a  cubical  cistern 
that  will  hold  160  hhds.  ? 

125.  What  is  the  interest,  at  h\%,  on  £2972  19s.  lid.  for 
11  y.  7  m.  23  d.  ? 

126.  I  sell  goods  for  $384  more  than  they  cost  me,  and  gain 
12|-%.    What  did  the  goods  cost  ? 

127.  A  monument  in  the  form  of  a  square  pyramid  is  2  ft. 
10  in.  -square  at  the  base,  and  is  11  ft.  high.  Allowing  175 
lbs.  to  the  cubic  foot,  what  is  the  weight  of  the  monument  ? 

128.  Lead  is  about  11  times  as  heavy  as  water.  Taking 
water  as  a  basis  (Ex.  18),  what  will  be  the  weight  of  135  rods 
of  lead  pipe  1  j  in.  in  diameter  and  |  in.  thick  ? 

129.  What  must  be  the  inside  diameter  of  a  globe  that  will 
contain  5  gals,  of  water  ? 

130.  A  man  has  three  farms,  the  first  of  which  contains 
28  A.  2  r.  6i  p. ;  the  second,  45  A.  1  r.  8  p. ;  and  the  third,  65  A. 
3  r.  The  cost  of  the  first  was  $45  per  acre ;  of  the  second, 
$80 ;  and  of  the  third,  $35.  He  sells  the  whole  at  $55  per 
acre.    Did  he  lose  or  gain,  how  much,  and  what  %  ? 

131.  A  and  B  carry  a  weight  of  360  lbs.  suspended  on  a  pole 
between  them,  4  ft,  long.  If  the  weight  is  removed  from  the 
centre  7  in.  towards  A,  how  much  does  each  carry  ? 

132.  When  money  is  worth  6%  per  annum,  do  I  gain  or 
lose,  and  what  %,  by  buying  merchandise  on  9  mos.  credit, 
and  selling  it  immediately  for  cash  at  the  same  price  ? 


90  AMTHMETICAL  EXAMPLES.  [CHAP.  IV. 

133.  What  is  the  weight  (see  Ex.  18)  of  an  iron  cylinder  8 
in.  in  diameter  and  22  ft.  long  ? 

131}.  Subtract  five  hundred  and  seventy-nine  thousand  eight 
hundred  and  ninety-one,  from  one  million  three  hundred  and 
sixty-two  thousand  four  hundred  and  sixty-seven,  and  multi- 
ply the  remainder  by  three  and  three  thousandths.  i 

135.  A  man  purchasing  a  barrel  of  flour  for  $9£,  14  lbs.  of 
sugar  at  13|  cts.,  and  a  pair  of  boots  for  $7.50,  hands  the 
shopkeeper  a  $20  bill.  How  much  should  be  returned  to 
him? 

136.  A  grocer  has  two  chests  of  tea,  each  weighing  60  lbs. ; 
one  costing  $45,  and  the  other  $84.  He  makes  the  price  so 
as  to  gain  20$,  and  sells  4  lbs.  of  the  former,  and  3  lbs.  of  the 
latter.    How  much  does  he  receive  ? 

137.  A  field  of  5  acres,  in  the  form  of  a  square,  is  to  be  sur- 
rounded by  a  board  fence  4A  ft.  high,  to  be  built  of  boards  8 
in.  wide,  the  lower  one  being  raised  2  in.  above  the  ground, 
and  with  a  space  of  3  in.  between  the  boards.  How.  many 
square  feet  of  boards  will  be  required  ? 

138.  When  hay  is  worth  $18  per  ton,  how  many  loads  of 
1500  lbs.  each  must  be  given  in  exchange  for  a  horse  valued 
at  $150,  and  a  carriage  worth  $120  ? 

139.  Add  all  the  odd  numbers  between  100  and  120,  and 
extract  the  cube  root  of  their  sum  to  the  second  decimal 
place. 

W  Find  the  value  of  ^J*/}  %+^y 

Ul.  If  6  men  dig  a  cellar  28  ft.  long,  18  ft.  wide,  and  10  ft. 
deep,  in  3  days  of  10  hours,  in  how  many  days  of  8  hours 
will  9  men  dig  a  cellar  42  ft.  long,  24  ft  wide,  and  8  ft.  deep  ? 

11$.  A  and  B  together  can  do  a  piece  of  work  in  14}  days, 
and  A  can  do  it  alone  in  25  days.  In  what  time  can  B  do  it 
alone  ? 

143.  Divide  fifty  and  fifty  ten-thousandths,  by  fifty  mil- 
lionths. 

144-  At  $1.75  per  sq.  ft.,  what  is  the  difference  in  the  value 
of  a  piece  of  land  87  ft.  by  42  ft,  and  one  57  ft  square  ? 


CHAP.  IV.]  AKITHMETICAL  EXAMPLES.  91 

145.  What  is  the  value  of  14  cwt.  3  qr.  15  lb.  of  iron  at 
$3.25  per  cwt.  ? 

146.  Multiply  52  A.  3  r.  13  p.  14  sq.  yd.  by  47. 

147.  A  note  was  given  March  4,  1868,  for  $1000,  on  which 
were  subsequently  made  the  following  indorsements :  Dec.  1, 
1868,  $75.  July  17,  1869,  $15.50.  Aug.  18,  1870,  $30.50. 
Dec.  11,  1870,  $500.  Jan.  3,  1871,  $150.  What  was  due 
Aug.  18, 1871  ? 

148.  If  the  interest  of  $1200  for  2  y.  3  mos.  is  $168.75,  what 
js  the  rate  ? 

149.  If  29}  yds.  of  cloth,  g  yd.  wide,  cost  $59,  what  will  be 
the  cost  of  21-J-  yds.,  of  the  same  quality,  1|  yds.  wide  ? 

150.  The  greater  of  two  numbers  is  7-J  times  the  less,  and 
their  sum  is  136.    What  are  the  numbers  ? 

151.  What  number  is  that  from  which  if  we  deduct  f  of 
itself,  and  %  of  the  remainder,  there  will  be  28  left  ? 

152.  How  much  interest  was  due  Dec.  11  upon  the  follow- 
ing accounts:  $200  due  March  19,  $200  due  March  24,  $1000 
due  March  25,  and  $600  due  April  10. 

153.  A  man  buys  goods  at  sundry  times  as  follows  :  May  1, 
a  bill  of  $800  on  4  mos.  May  15,  a  bill  of  $1200  on  6  mos. 
June  1,  a  bill  of  $1500  on  8  mos.  June  15,  $800  for  cash, 
and  gives  a  note  for  the  whole  at  60  days  with  interest.  What 
should  be  the  date  of  the  note  ? 

151/..  The  shadow  of  a  flagstaff  which  is  80  ft.  high  is  45  ft. 
6  in.  What  would  be  the  length  of  an  object  whose  shadow 
is  11  ft.  9  in.  ? 

155.  Find  the  prime  factors  of  8866. 

156.  A  kettle  of  hemispherical  shape  is  2  ft.  in  diameter. 
How  many  pailfuls,  of  3  gals,  each,  will  it  contain  ? 

157.  A  merchant  who  has  flour,  the  cost  price  of  which  is 
$9.75  per  bbl.,  exchanges  it  with  a  farmer  for  potatoes,  at  85 
cts.  per  bushel,  on  condition  that  the  price  of  the  flour  shall 
be  advanced  h%,  and  the  farmer  shall  deduct  the  same  %  on 
his  potatoes.  How  many  bushels  of  potatoes  will  be  required 
to  pay  for  2  bbls.  of  flour  ? 


92  AEITHMETICAL   EXAMPLES.  [CHAP.  IV. 

158.  How  many  miles  are  there  in  47.8326  kilometers  ? 

159.  What  is  the  surface  of  a  sphere  whose  diameter  is  18 
inches  ? 

160.  If  18  days'  work  will  pay  for  2  hhds.  of  molasses,  and 
8  hhds.  of  molasses  are  worth  12  tons  of  hay,  and  3  tons  of 
hay  will  purchase  2  hags  of  coffee,  and  8  hags  of  coffee  are 
worth  40  yds.  of  cloth,  how  many  yds.  of  cloth  can  be  bought 
for  9  days'  labor  ? 

161.  How  many  hectoliters  will  a  box  contain  whose  length 
is  2.25  meters,  width  1.75  meters,  and  depth  1  meter? 

162.  If  22^  of  a  merchant's  sales  is  profit,  what  %  does  he 
gain  ? 

163.  An  army  of  6000  men  was  supplied  with  12  days' 
rations  at  30  ounces  per  day  for  each  man.  At  the  end  of  6 
days  1000  men  have  been  lost,  and  it  is  required  to  make  their 
rations  last  9  days  longer.  What  will  be  each  man's  daily 
allowance  ? 

16Jf.  If  60  reams  of  paper  will  print  3000  pamphlets,  of  10 
sheets  each,  how  many  reams  will  print  1480  pamphlets  of 
12^  sheets  each  ? 

165.  The  rafters  of  a  building  24  ft.  wide  are  20  ft  long. 
How  high  is  the  gable  end  ? 

166.  Goods  are  bought  to  be  paid  for  as  follows:  |  in  8 
mos.,  I  in  6  mos.,  and  the  remainder  in  9  mos.  What  will  be 
the  equated  time  for  the  payment  of  the  whole  ? 

167.  Four  men  are  in  partnership  for  one  year,  and  their 
united  capital  is  $42000.  The  first  man  puts  in  his  capita] 
Jan.  1 ;  the  second,  Feb.  1 ;  the  third,  April  1 ;  and  the  fourth. 
May  1.  At  the  end  of  the  year,  they  have  all  gained  an  equal 
sum.     What  was  the  capital  of  each  man  ? 

168.  How  many  hectares  are  there  in  a  piece  of  land  A  mile 
square  ? 

169.  If  I  wish  to  obtain  from  a  bank  $1500,  for  what  sum 
must  a  note  be  given  for  90  days  ? 

170.  The  solid  contents  of  a  sphere  are  268.08  cubic  inches. 
What  is  the  diameter  ? 


CHAP.  IV.]  ARITHMETICAL  EXAMPLES.  93 

171.  A  piece  of  land  containing  2  acres  is  5  times  as  long  as 
it  is  broad.     What  are  the  length  and  the  breadth  ? 

172.  If  8  men  saw  30  cords  of  maple  wood  in  the  same  time 
as  10  men  saw  28  cords  of  oak,  and  if  6  men  saw  36  cords  of 
oak  in  4  days  of  9  hours  each,  how  many  hours  a  day  must  7 
men  work  to  saw  90  cords  of  maple  wood  in  6  days  ? 

173.  How  many  kilometers  are  there  in  26589  meters  ?    ■ 

171f.  Eind  35%  of  the  area  of  a  piece  of  land  46  rods  long 
and  17  rods  wide. 

175.  What  sum  should  be  discounted  for  the  present  pay- 
ment of  $1800  due  in  10  months  ? 

176.  In  a  certain  school  y1^  of  the  pupils  are  under  12  years 
of  age ;  £  between  12  and  14 ;  \  between  14  and  16 ;  T\  be- 
tween 16  and  18 ;  and  27  are  over  18.  What  is  the  whole 
number  of  pupils  ? 

177.  If  coal  costs  $4. 62 J  per  ton  at  the  mine,  and  the 
freight,  insurance,  unloading,  &c,  cost  $2.87J  per  ton,  at  what 
price  should  it  be  sold  to  gain  16%  ? 

178.  What  sum  of  money  must  a  man  lay  up  annually 
which  shall  amount,  at  6%  compound  interest,  to  $10000  in 
20  years  ? 

179.  Extract  the  cube  root  of  205,692,449,327. 

180.  A  room  is  16  ft.  long,  14£  ft.  wide,  and  10  ft.  high. 
What  is  the  distance  between  an  upper  corner,  and  the  oppo- 
site lower  corner  ? 

181.  The  circumference  of  a  circle  is  3  ft.  4  in.  What  is  the 
side  of  a  square  of  equal  area  ? 

182.  I  owe  a  note  of  $2500  in  Savannah,  which  has  been  on 
interest  8  mos.  at  7%.  If  exchange  is  101|,  what  wili  be  the 
face  of  a  sight  draft  to  pay  the  note  and  interest  ? 

183.  A  merchant  sells  flour  at  $7.92  per  bbl.,  and  loses  \%. 
At  what  price  should  it  be  sold  to  gain  8%  ? 

18 If.  A  man  purchases  12  books,  the  first  of  which  costs  60 
cents,  and  the  second,  65  cents,  and  so  on  in  arithmetical 
progression.     What  is  the  cost  of  the  whole  ? 


94  ARITHMETICAL  EXAMPLES.  [CHAP.   IV. 

185.  What  must  be  the  diameter  of  a  cylindrical  cup  6  in. 
high  to  hold  a  gallon  ? 

186.  If  I  purchase  a  yoke  of  oxen  on  4  mos.  credit  for  8180, 
and  sell  them  immediately  for  $192  cash,  what  %  do  I  gain, 
when  the  rate  of  interest  is  6%  ? 

187.  A  man  being  asked  the  time  of  day,  said  that  ft  of  the 
time  before  midnight  was  equal  to  £  the  time  past  noon. 
What  was  the  time  ? 

188.  What  must  be  the  depth  of  a  cylindrical  measure  18^ 
in.  in  diameter,  to  contain  a  bushel  ? 

189.  Bought  a  piece  of  land  65  rods  long  and  38  rods  wide, 
for  $600,  from  which  I  sold  8  acres  2  roods  10  rods,  at  $60 
per  acre.  I  then  sold  the  remainder  for  $446,875.  At  what 
price  per  acre  was  the  last  lot  sold  ? 

190.  In  a  triangular  field  of  corn  which  commences  at  one 
of  the  angles  with  a  single  hill,  and  with  three  hills  in  the 
row  next  to  it,  there  are  41  rows.  How  many  hills  are  there 
in  the  field  ? 

191.  A  cylindrical  ash  barrel  is  made  15  inches  in  diameter 
and  25  inches  high.     How  many  bushels  will  it  contain  ? 

192.  In  Example  191,  how  many  square  feet  of  sheet  iron 
were  required  to  make  the  ash  barrel,  allowing  in  the  circum- 
ference and  in  the  diameter  of  the  bottom,  1  inch  for  lapping 
at  the  joint  ? 

193.  When  gold  is  at  110f,  what  is  the  gold  value  of  $6000 
in  currency  ? 

191f.  Find  the  cube  root  of  8*. 

195.  Divide  the  difference  between  T3g  and  four  millionths, 
by  .0001. 

196.  What  is  the  capacity,  in  gallons,  of  a  cask  26  in.  long, 
and  head  and  bung  diameters  17  and  22  inches  ? 

197.  What  will  be  the  cost,  at  $8.25  per  cord,  of  a  pile  of 
wood  14  ft.  long,  7  ft.  4  in.  high,  and  4  ft.  wide  ? 

198.  How  many  bricks  will  be  required  to  construct  the 
walls  and  chimneys  of  a  house  of  the  following  dimensions  ? 
Length,  42  ft;  width,  24  ft.;  height,  lirl  It.;  height  of  the 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  95 

gable  ends,  11  ft. ;  thickness  of  the  walls,  1  foot.  There  are 
to  be  three  doors,  each  44-  ft.  by  8  ft. ;  12  windows,  4  ft.  by 
6£;  and  14  windows,  3  h  ft.  by  5 \.  There  are  to  be  two 
chimneys,  built  from  the  bottom  of  the  cellar,  which  is  8  ft. 
deep,  to  extend  7  feet  above  the  ridge  of  the  roof,  each  24  by 
16  inches. 

199.  How  many  yds.  of  carpeting,  |  yd.  wide,  will  be  neces- 
sary to  carpet  a  room  18  ft.  4  in.  long,  and  15  ft.  wide  ? 

200.  A  bin  for  grain  is  8  ft.  long,  and  4  ft.  wide.  How 
high  must  it  be  to  contain  275  bushels  ? 

201.  Bought  60  shares  of  railroad  stock  at  97,  and  sold  the 
same  at  par  after  receiving  a  dividend  of  21%.  What  was  my 
whole  gain,  and  what  the  gain  %  on  my  investment  ? 

202.  If  4  compositors  in  6  days  of  10  hours  can  set  90  pages 
of  types,  each  page  containing  36  lines  of  50  letters,  how  many 
compositors  will  be  required  to  set  360  pages,  each  page  con- 
taining 40  lines  of  54  letters,  in  8  days  of  8  hours  ? 

203.  When  gold  is  at  112J,  and  exchange  on  Paris  at  5.16, 
what  is  the  face  of  a  bill  on  Paris  that  can  be  bought  with 
18000  in  currency  ? 

20Jf.  A  boy  spent  1  cent  on  Monday,  2  cts.  on  Tuesday,  4 
cts.  on  Wednesday,  and  so  on  for  every  week-day  for  a  fort- 
night. How  much  did  he  spend  the  last  day,  and  how  much 
in  all  ? 

205.  What  is  the  accurate  interest  on  a  government  bond 
of  $5000  at  7T30^,  from  Jan.  1  to  March  1,  inclusive,  1872  ? 

206.  A  railroad  has  a  capital  stock  of  $28,000,000.  Its 
transactions  for  the  year  ending  October  31, 1870,  were  as  fol- 
lows :  Receipts — From  passengers,  $4,032,023.39 ;  from  freight, 
$9,151,750.42 ;  from  mails,  expresses,  and  all  other  sources, 
$795,740.19.  Expenditures  —  Repairing  and  maintaining 
roadway  and  real  estate,  fences,  and  taxes  on  real  estate, 
$3,558,143.04 ;  repairing  engines,  tenders,  passenger  and 
freight  cars ;  tools,  oil,  fuel,  watchmen,  &c,  $2,728,968.58 ; 
operating  the  road,  including  salaries,  agencies,  oil,  fuel, 
water,  general  superintendence,  and  contingent  expenses, 
$4,366,580.77.     The  corporation  also  paid  §%  interest  on  a 


9G  AEITHMETICAL  EXAMPLES.  [CHAP.   IV. 

debt  of  $12,000,000;  and  certain  other  items  of  interest 
amounting  to  $223,880.66  ;  for  rent  of  branch  roads, 
$226,848.04;  United  States  tax  on  passenger  earnings  and 
dividends,  $172,904.88 ;  and  it  was  decided  to  reserve,  for 
contingent  purposes,  at  least  $300,000,  before  declaring  a  divi- 
dend. What  dividend,  omitting  fractions  of  C/Ci  was  declared, 
and  what  was  the  exact  amount  of  surplus  reserved  ? 

207.  Bought  a  piece  of  cloth  which  proved  to  be  but  g  at 
long  as  it  was  marked ;  but  I  find  that  if  I  sell  it  at  $G  per 
yd.,  I  shall  gain  5%  on  the  first  cost.  What  did  the  cloth 
cost  per  yd.  ? 

208.  Bought  a  bill  of  goods  amounting  to  $6845,  and  after 
paying  charges,  $65,  I  sold  the  same  at  an  advance  of  12 
and  took  a  note  for  60  days  which  I  had  discounted  at  a  bank 
at  6^,  and  with  the  proceeds  bought  a  bill  on  London,  ex- 
change being  at  109.J.     What  was  the  face  of  the  bill  ? 

209.  When  b%  government  bonds  are  quoted  at  104,  what 
sum  must  be  invested  to  yield  an  annual  income  of  $800  ? 

210.  After  disposing  of  7  A.  3  r.  13  p.  of  land  to  one  man, 
and  16  A.  1  r.  35  p.  to  another,  I  find  I  have  sold  23^  of  my 
farm.     How  much  have  I  left  ? 

211.  If  a  carriage  wheel  turns  6  \  times  in  going  6i  rods, 
how  many  times  will  it  turn  in  going  2  J  miles  ? 

212.  A  ladder  20  ft.  long,  standing  12  ft.  from  a  house  at 
the  bottom,  leans  against  the  house,  4  ft.  below  the  eaves. 
How  high  is  the  house,  and  how  much  must  the  ladder  be 
lengthened  to  reach  1  foot  above  the  eaves  ? 

218.  Two  pieces  of  cloth  were  originally  of  the  same  length  : 
but  after  15  yds.  had  been  sold  from  one,  and  24  yds.  from 
the  other,  the  shorter  piece  was  found  to  be  f  of  the  other. 
What  was  the  original  length  ? 

211/..  Two  men,  A  and  B,  100  miles  apart,  arc  traveling 
towards  each  other,  A  at  the  rate  of  16]  miles  in  5  hours,  and 
B  at  the  rate  of  10£  miles  in  3  hours.  If  A  trawls  2  hours 
before  B  sets  out,  how  far  will  each  travel  before  they  meet? 

215.  On  what  day  will  88(50,  put  at  <','/  interest  Jan,  1, 
amount  to  $900  ? 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  97 

216.  A  and  B  trade  in  partnership  and  their  profits  amount 
to  $2280 ;  of  which  A's  share  is  $960.  B's  capital  is  $11000. 
How  much  capital  had  A  ? 

217.  Sold  a  quantity  of  goods  for  $1100,  thereby  losing  10$, 
whereas  I  had  expected  to  gain  15$.  What  was  my  whole 
loss? 

218.  A  garrison  of  400  men  is  supplied  with  provisions  for 
8  months.  At  the  end  of  2  months  it  was  decided  to  reduce 
the  garrison  so  as  to  make  the  provisions  last  12  months  from 
that  time.     How  many  men  were  sent  away  ? 

219.  Amos  Brown  gave  a  note,  Nov.  1,  1870,  to  Thomas 
Wells  for  $1800,  with  interest  at  6$.  On  this  note  the  follow- 
ing indorsements  were  subsequently  made :  Jan.  25,  1871, 
$265 ;  March  1,  1871,  $18 ;  April  1,  1871,  $7.50 ;  June  15, 
1871,  $1100  ;  Sept.  1,  1871,  $30 ;  Oct.  10,  1871,  $300.  Soon 
after  the  last  payment,  Brown  failed,  and  Wells  agreed  to  re- 
linquish the  note  for  75  cts.  on  the  $.  What  did  he  receive  at 
settlement,  Dec.  7, 1871  ? 

220.  The  circumference  of  a  circular  pond  is  100  rods. 
What  is  its  diameter,  and  its  area  ? 

221.  A  person  buys  90  apples  at  2  for  a  cent  and  90  at  3 
for  a  cent.  Does  he  gain  or  lose,  and  how  much,  by  selling 
the  whole  at  5  for  2  cents  ? 

222.  Three  persons,  A,  B  and  C,  travel  in  the  same  direc- 
tion around  an  island  45  miles  in  extent ;  A,  at  the  rate  of  3 
miles ;  B,  4  miles,  and  C,  5  miles,  per  hour.  In  what  time 
will  they  be  together  at  the  place  where  they  set  out,  traveling 
10  hours  per  day,  and  how  far  will  each  have  traveled  ? 

223.  Eequired  the  contents  of  the  following  lot  of  lumber, 
and  the  cost,  at  $18  per  M. ;  12  boards,  13  ft.  6  in.  long,  and 

15  in.  wide ;  10  boards,  22  ft.  long,  12  in.  wide ;  4  stocks,  12 
boards  each,  15  ft.  long,  11  in.  wide ;  13  boards,  12  ft.  long, 

16  in.  wide  at  one  end,  and  12  in.  at  the  other  ? 

22J+.  Mixed  45  bushels  of  corn  at  .95,  with  30  bushels  at 
$1,  and  25  bushels  at  $1.05.  At  what  prioe  per  bushel  must 
the  mixture  be  sold  to  gain  5%  ? 

5 


98  ARITHMETICAL    EXAMPLES.  [«'JIAI\   IV. 

225.  A  note  for  $800,  without  interest,  due  Sept.  15,  1872, 
was  paid  May  1,  1872.     What  was  the  discount,  money  being 

worth  7$  ? 

226.  A  man  divided  $16500  among  three  children  in  such 
a  manner  that  the  second  was  greater  by  one-half  than  tho 
first,  and  \  of  the  first  was  \  of  the  third.  What  was  the  share 
of  each  ? 

227.  A  man  imports  60  pieces  of  broadcloth,  14  yds.  each, 
at  $2.75  per  yd.  The  duties  and  other  charges  amounted  to 
$640.     At  what  price  per  yd.  must  he  sell  it  to  gain  15$  ? 

228.  A  man  has  a  stack  of  hay  12  ft.  in  diameter,  and  18  ft. 
high.  The  sides  are  perpendicular  to  the  height  of  12  ft, 
above  the  ground,  and  the  remainder  of  the  stack  is  conical  in 
shape.  Allowing  12  cubic  yds.  to  the  ton,  what  is  the  weight 
of  the  whole  stack  ? 

229.  Keduce  £468  10s.  4d.  to  United  States  money,  ex- 
change being  at  108f ,  and  find  the  interest  on  the  same,  at 
1%  for  4  months  8  days. 

230.  Change  8  lbs.  4  oz.  Avoirdupois  weight  to  Troy  weight. 

231.  The  interest  on  a  certain  sum  for  1  mo.  13  d.,  at  7$,  is 
$4.05.     What  is  the  principal  ? 

232.  If  I  buy  railroad  stock  at  109A,  and  receive  annually  a 
dividend  of  1%,  what  %  do  I  receive  on  my  investment  ? 

233.  Bought  a  house  and  lot  for  $6000.  For  what  must  1 
rent  it  to  gain  6%  on  my  money,  and  to  pay  $25  for  repairs, 
$22.50  for  insurance,  and  taxes  at  \\c/0  on  J  of  the  valuation  ? 

234.  A  bill  of  goods  for  $4200,  on  4  mos.  credit,  is  offered 
for  $4110,  ready  cash.  Do  I  gain  or  lose,  and  how  much,  by 
taking  them  at  the  cash  price,  money  being  worth  6g  ? 

235.  How  many  feet  of  boards  will  be  required  to  co\<  r  n 
building,  including  the  roof,  46  ft.  long,  23  ft.  wide,  19i  ft. 
high ;  the  height  of  the  roof  being  12  ft.  ? 

236.  A  note  was  given  Sept.  4, 1870,  for  $1300,  with  interest 
at  n%.  July  12, 1871,  a  payment  of  $575.50  was  made.  What 
was  due  April  1, 1872  ? 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  99 

237.  How  many  shingles  will  be  necessary  to  cover  the  roof 
of  a  building  45  ft.  long,  25  ft.  wide,  height  of  roof  18  ft. ; 
allowing  that  the  shingles  average  3|  in.  in  width,  and  are  to 
be  laid  5  in.  to  the  weather ;  also  that  the  roof  projects  If  ft. 
over  the  eaves,  and  1\  ft.  at  each  end  ? 

238.  What  are  the  contents,  in  board  measure,  of  4  planks, 
18  ft.  long,  15  in.  wide,  and  3  in.  thick  ? 

239.  Eeduce  5  hectares  to  square  rods. 

240.  When  gold  is  at  112J,  exchange  on  Havana  at  Z\% 
premium,  and  brokerage  \%,  what  will  be  the  cost  in  currency 
of  a  draft  on  Havana  for  $22500  ? 

gjl.  Extract  the  square  root  of  the  product  of  the  squares 
of  11  and  16. 

2Jf2.  If  a  piece  of  work  can  be  done  by  4  men  in  3  days ; 
or  by  6  women  in  2h  days  ;  or  by  7  boys  in  4  days ;  in  what 
time  can  a  man,  a  woman,  and  a  boy  do  it  together  ? 

243.  For  what  sum  must  a  bank  note  be  given  for  60  days, 
to  obtain  the  money  to  pay  for  the  following  bill  of  goods:  77 
pieces  sheeting,  31J  yds.  each,  at  7£  cts. ;  8  pieces  of  broad- 
cloth, 14  yds.  each,  at  $3.62£ ;  5  J  doz.  shawls,  at  $66  per  doz.  ? 

244.  Goods  are  marked  at  25%  advance  on  the  cost,  but  are 
sold  at  a  discount  of  15%  on  the  asking  price.  What  is  the 
gain  %  ? 

245.  What  is  the  difference  between  the  area  of  a  square 
circumscribed  about  a  circle  18  in.  in  diameter,  and  the  area 
of  the  largest  square  that  can  be  inscribed  within  the  same 
circle  ? 

246.  With  $12000  I  purchased  a  draft  on  New  Orleans  at 
\%  premium,  which  I  sent  to  my  agent  there  to  pay  for  cotton 
purchased  for  me  at  %\%  commission.  What  was  the  value  of 
the  cotton  purchased  ? 

247.  A  man  divides  4  A.  1  r.  36  p.  into  28  building  lots. 
What  will  be  the  cost  of  one  of  those  lots  at  62h  cts.  per  sq. 
ft.? 

248.  A  pile  of  wood  which  contains  4£  cords,  is  7  ft.  6  in, 
high,  and  4  ft.  wide.     What  is  the  length  ? 


100  ARITHMETICAL  EXAMPLES.  [CHAP.   IV. 

2Jf9.  For  what  sum  must  a  bank  note  be  drawn  for  60  days, 
at  6%,  to  make  immediate  payment  of  a  demand  of  $1200  due 
in  8  mo.  15  d.  ? 

250.  What  is  the  bank  discount  on  a  note  of  $800  for  3 
mos.  ? 

251.  If  I  buy  flour  at  $8.50  per  bbl.,  and  retail  it  at  the 
rate  of  20  lbs.  for  $1,  what  is  my  gain  %  ? 

252.  When  money  is  worth  6$,  what  can  I  afford  to  pay  for 
railroad  stock  that  yields  a  dividend  of  5%  semi-annually  ? 

253.  At  what  %  will  $750  amount  to  $847.03  in  2  y.  3  mos.  ? 
251+.  If  I  compromise  with  an  insolvent  creditor  at  70  cts. 

on  the  $,  and  then  discount  2%  for  immediate  payment,  what 
is  my  total  loss  on  a  demand  of  $6500  ? 

255.  If  I  purchase  for  112,  U.  S.  5-20's  which  bear  interest 
at  the  rate  of  6%  in  gold,  payable  semi-annually,  when  gold  is 
at  110§,  and  after  keeping  them  1  year,  sell  them  at  111}, 
what  %  do  I  make  on  my  investment  ? 

256.  |  of  a  certain  number  exceeds  J  of  the  same  number 
by  10.     What  is  the  number  ? 

257.  If  12  men  can  perform  a  piece  of  work  in  18  days, 
how  many  men  will  be  required  to  perform  a  piece  of  work  3 
times  as  large  in  12  days  ? 

258.  If  a  certain  number  is  doubled,  and  the  product  di- 
vided by  3,  and  the  quotient  squared,  and  that  square  in- 
creased by  \  of  itself,  the  result  will  be  \  of  the  square  of  12. 
What  is  the  number  ? 

259.  In  4  yrs.  6  mos.  a  sum  of  money  at  7T30$  amounted  to 
$956.87.     What  was  the  sum  ? 

260.  A  man  offered  a  bill  of  goods  for  $1800  on  6  mos.  credit, 
or  for  the  present  worth  of  that  sum  for  cash.  I  accepted  the 
latter  offer,  and  obtained  the  money  at  a  bank  for  the  same 
time  at  6%.     Did  I  lose  or  gain,  and  how  much  ? 

261.  What  will  it  cost  to  insure  a  house  worth  $6000,  at  \% 
on  |  of  its  valuation,  and  $1800  worth  of  furniture  at  \%  on  \ 
of  its  value,  allowing  $1  for  the  cost  of  the  policy  ? 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  101 

262.  What  is  9$  of  eleven  thousand  eleven  hundred  and 
eleven  dollars? 

263.  A  merchant's  sales  average  15$  profits,  and  his  losses 
by  bad  debts  amount  to  $1500.  "What  is  the  amount  of  his 
sales,  if  his  net  income  is  $3100  ? 

264-  What  is  the  accurate  interest  on  $1400,  at  6$,  for  the 
month  of  July  ? 

265.  If  I  hire  money  at  a  bank  for  4  mos.,  at  6$,  with 
which  to  purchase  a  horse  at  $180,  what  does  the  horse  really 
cost  me  ? 

266.  How  many  days  are  there  in  5$  of  the  year  1872  ? 

267.  What  is  the  least  common  multiple  of  the  numbers  1 
to  12  inclusive  ? 

268.  What  quotient  will  be  obtained  by  dividing  the  cube 
of  75  by  the  J  part  of  1000  ? 

269.  What  profit  do  peaches  pay  at  2  cts.  apiece,  which  cost 
60  cts.  per  hundred,  if  10$  of  them  are  lost  by  decay  ? 

270.  What  is  the  board  measure  of  4  sticks  of  timber  12  by 
10  in.  and  18  ft.  long?-^' 

271.  What  will  it  cost,  at  30  cts.  per  centiare,  to  plaster  a 
hall  76  ft.  long,  54  ft.  wide,  and  18  ft.  high,  deducting  10$  for 
windows,  doors,  and  base  ? 

272.  Compute  the  duties  on  the  following  articles :  8  casks 
of  raisins,  at  11  cts.  per  lb.,  gross  weight  888  lbs.,  tare  12  lbs. 
per  cask,  duty  25$  ad  valorem;  12  boxes  sugar,  400  lbs.  each, 
at  7  cts.  per  lb.,  tare  10$,  duty  24$  ad  valorem;  60  hhds. 
molasses,  63  gals,  each,  at  54  cts.  per  gal.,  leakage  2$,  duty 
20$ ;  1  box  books,  75  vols.,  at  5  cts.  per  vol. 

273.  A  note  of  $400  was  given  Jan.  1, 1871,  at  6$  interest, 
on  which  a  payment  of  $25  was  made  the  first  of  each  subse- 
quent month  during  the  year.    What  was  due  Jan.  1,  1872  ? 

21 ']/..  The  difference  in  time  between  Boston  and  San  Fran- 
cisco is  3  h.  25  m.  31  s.    What  is  the  difference  in  longitude  ? 

275.  If  by  selling  cloth  at  $4.75, 1  lose  8$,  at  what  price 
must  it  be  sold  to  gain  12*$  ?- 


102  ARITHMETICAL   EXAMPLES.  [CHAP.   IV. 

276.  A  and  B  are  in  trade  ;  A's  capital  is  twice  that  of  B's. 
B  gains  50$,  and  A  loses  $4000,  when  A  has  §  as  much  as  B. 
What  was  the  original  capital  ? 

277.  What  will  be  the  proceeds  of  a  bank  note  for  90  days, 
for  $625,  at  7$  ? 

278.  If  I  own  T3g  of  a  ship  which  is  worth  $18000,  what 
part  .shall  I  have  left,  after  selling  \  of  %  of  my  share,  and 
what  will  it  be  worth  ? 

279.  The  cube  of  3.5  is  the  square  root  of  what  number  ? 

280.  A  railroad  company  has  %  of  an  acre  of  land  covered 
with  wood  11  ft.  high.     How  many  cords  are  there  ? 

281.  A,  B,  and  C  trade  in  company.  A  puts  in  \  of  the 
capital,  B  X,  and  C  the  remainder.  How  shall  a  gain  of 
$2150  be  divided  among  them  ? 

282.  How  many  times  does  a  common  clock  strike  in  24 
hours  ? 

288.  A  school  has  an  annual  income  of  $1200,  and  receives, 
once  in  15  years,  $1396  for  renewing  furniture.  What  is  the 
amount  of  its  funds  invested  at  6%  ? 

28^.  My  agent  in  Liverpool  sends  me  a  bill  of  goods,  pur- 
chased by  my  order  for  £2000,  and  charges  me  If  $  commis- 
sion. What  will  be  the  cost  of  a  bill  of  exchange  to  pay  the 
bill,  the  course  of  exchange  being  108  J  ? 

285.  A. town  votes  to  raise,  for  sundry  purposes,  $18750. 
Allowing  3%  for  collecting,  for  what  sum  must  the  tax  be 
levied  ? 

286.  What  is  the  amount  of  $11925.76  for  4  y.  7  mos.  19  d. 
at7f$? 

287.  A  draft  on  Liverpool  for  £1000  cost  $5525.33  in 
currency,  when  gold  was  at  112.  What  was  the  rate  of 
exchange  ? 

288.  When  gold  is  at  110f,  what  will  be  the  cost  in  cur- 
rency of  375  M.  of  lumber  in  Montreal  at  $26  per  U.  ? 

289.  If  a  man  pays  a  tax  of  5%  on  his  income  over  $1000, 
and  after  paying  his  tax  has  remaining  in  all  $3710,  what  is 
his  whole  income  ? 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  103 

290.  A,  B,  and  0  can  do  a  piece  of  work  in  10  days,  and  B 
and  C  can  do  it  in  18  days.    In  what  time  can  A  do  it  alone  ? 

291.  A  man  who  owes  $27500,  becomes  insolvent,  and  his 
assets  are  $11200.  The  expenses  of  settling  are  $525.  What 
will  be  the  rate  of  the  dividend,  and  what  will  a  man  receive 
who  has  a  claim  for  $3600  ? 

292.  A  speculator  purchases  6  hectares  of  land  for  $1050, 
and  divides  it  into  lots  of  8  ares  each.  What  must  be  the 
price  per  lot  to  gain  30%  ? 

293.  The  distance  between  the  opposite  corners  of  a  square 
field  is  50  rods.     How  many  acres  does  it  contain  ? 

294-.  If  I  wish  to  make  a  payment  of  $50  the  first  of  each 
month  from  Jan.  to  July,  and  one  of  $100  per  month  from 
Aug.  to  Dec,  at  what  time  can  I  make  the  whole  in  one 
payment  ?■ 

295.  How  many  bricks  of  the  ordinary  size  will  be  required 
to  pave  a  yard  6  rods  long  and  4  rods  wide  ? 

296.  What  will  be  the  amount  of  $600  at  ty%  compound 
interest  for  5  years  ? 

297.  What  %  do  I  make  by  purchasing  flour  at  $7.50  per 
bbl.,  cash,  and  selling  the  same  for  $8.25  on  3  mos.  credit, 
money  being  worth  Q>%  ? 

298.  On  a  note  of  $750,  dated  Jan.  1,  a  payment  was  made 
July  15,  that  was  $13  more  than  the  interest  then  due  ;  and 
another  payment  of  $300  was  made  Sept.  25.  What  was  due 
Oct.  12,  and  what  was  the  payment  of  July  15  ? 

299.  How  many  bushels  of  wheat  will  a  hhd.  of  63  gals, 
capacity  contain  ? 

300.  My  agent  in  New  York  has  sold  for  me  an  invoice  of 
lumber  amounting  to  $22850,  charging  me  3%  commission. 
One-half  the  proceeds  he  remitted  to  me  by  draft,  charging 
\%  brokerage,  and  with  the  other  half  he  purchased  for  me 
molasses  at  .46  per  gal.,  and  charged  2%  commission.  How 
many  hhds.  of  molasses  did  he  ship  to  my  order,  and  what  was 
the  amount  of  the  draft  sent  ? 


104  ARITHMETICAL  EXAMPLES.  [CHAP.   IV. 

301.  A  man  sold  goods  at  a  gain  of  12^%,  and  invested  the 
proceeds  and  sold  at  an  advance  of  8% ;  then  invested  again 
and  sold  at  a  loss  of  b%,  when  he  had  $9018.75  left  What 
was  his  original  capital  ? 

802.  Extract  the  cube  root  of  the  square  of  the  largest 
number  that  can  be  written  with  three  figures. 

803.  A  man  left  $8000  to  be  divided  between  two  sons, 
aged  16  and  18  respectively,  in  such  a  way  that  the  parts 
being  put  out  at  6%  simple  interest,  should  amount  to  equal 
sums  when  the  sons  respectively  should  become  of  age.  What 
were  the  parts  ? 

804.  What  decimal  of  a  rod  is  .285  of  a  foot  ? 

305.  The  area  of  a  cubic  block  is  384  inches.  What  is  the 
length  of  a  diagonal  of  one  of  its  faces  ? 

306.  Bought  a  note  for  50  cts.  on  the  $,  and  then  collected 
13%  more  than  I  paid,  and  thereby  gained  $112.  What  was 
the  face  of  the  note,  and  what  amount  did  I  collect  ? 

807.  WTiat  is  15%  of  the  difference  between  the  second  root 
of  256,  and  the  second  power  of  the  same  number  ? 

308.  A  man  received  $85.25  interest  on  $1265,  at  6%.  What 
was  the  time  ? 

809.  Reduce  *  of  2±  +  (fr  of  |  x  H)  x  10*. 

310.  How  many  steps,  each  2  ft.  8  in.,  will  a  man  take  in 
walking  from  Boston  to  »New  York,  265  miles  ? 

311.  Find  the  sum,  difference,  and  product,  of  6  J  and  12j53  ; 
also  the  sum  of  those  three  results. 

812.  What  is  the  board  measure  of  the  largest  square  tim- 
ber that  can  be  sawn  from  a  log  16  ft.  long  and  17  in.  in 
diameter  ? 

813.  How  many  square  feet  of  surface  in  a  stove  pipe  16  ft 
long  and  7  in.  In  diameter  ? 

8 14.  A  can  build  a  piece  of  wall  in  16  days,  and  A  and  B 
together  can  build  it  in  10  days.  After  \  of  the  wall  is  built, 
in  what  time  can  B  finish  it  ? 

815.  A  note  of  $600  was  given  Jan.  1,  at  6%  interest,  on 
which  a  payment  of  $225  was  made  July  3.     Oct.  15  the  note 


CHAP.  IV.]  ARITHMETICAL   EXAMPLES.  105 

was  purchased  at  Z%  discount  on  its  value  at  that  time.    What 
sum  was  paid  for  it  ? 

816.  A  man  has  a  bin  28  ft.  long,  5  ft.  4  in.  wide,  and  4  ft. 
deep,  filled  with  wheat.    What  is  it  worth,  at  $1.10  per  bushel  ? 

817.  In  how  many  days  will  $75,  at  7^%  interest,  gain  .80  ? 

818.  If  a  ball  3  in.  in  diameter  weighs  8  lbs.,  what  will  be 
the  weight  of  another  ball  5£  iu.  in  diameter,  made  of  material 
20%  heavier  than  the  first-named  ball  ? 

819.  %  of  A's  money  and  -f  of  B's  money  equal  $900 ;  and 
|  of  B's  is  twice  -§  of  A's.    What  sum  has  each  ? 


I  What  is  the  cost,  at  $9.50  per  cord,  of  a  pile  of  wood 
4  ft.  wide,  6  ft.  high,  34  ft.  long  at  the  bottom,  and  24  ft.  at 
the  top  ? 

821.  After  a  rainfall  of  §  of  an  inch,  how  many  hhds.  of 
water  will  a  cistern  contain  which  drains  the  roof  of  a  build- 
ing 65  ft.  by  34  ft.  ? 

822.  Divide  g  of  -f-  of  17|  by  T%  of  4|. 

1 1 

828.  Multiply  the  difference  between  4.4  and  .00027  by  the 
product  of  2.1  and  .005. 

824.  A  note  of  $400  is  dated  Jan.  1, 1871,  on  which  was 
indorsed  June  4, 1871,  $150,  and  Oct.  9, 1871,  $60.  What 
was  due  April  26,  1872,  the  rate  of  interest  being  6%  ? 

825.  Bought  150  boxes  of  raisins  at  5%  less  than  the  first 
cost  and  sold  them  at  5%  advance  on  the  first  cost,  and  thereby 
gained  $45.    What  was  the  first  cost  per  box  ? 

826.  What  will  it  cost,  at  18  cents  per  square  yard,  to  paint 
the  outside  of  a  house  40  ft.  long,  26  ft.  wide,  and  18  ft.  high, 
the  height  of  the  roof  being  13  ft.,  and  there  being  no  allow- 
ance for  doors  and  windows  ? 

827.  I  have  due  me  $12000 ;  \  in  5  mos.,  |  in  9  mos.,  and 
the  remainder  in  15  mos.  What  is  the  present  value  of  the 
whole  debt  ? 

>  828.  If  it  require  800  yds.  of  cloth,  1£  yds.  wide,  to  clothe 
340  soldiers,  how  many  yds.,  five-fourths  wide,  will  be  neces- 
sary to  clothe  430  soldiers  ? 

5* 


106  AKITHMETICAL  EXAMPLES.  [CHAP.    IV. 

829.  Divide  2g  times  $  of  29^  by  4|  times  T30  of  8. 

830.  A  square  field  containing  6h  acres  is  surrounded  by  a 
close  board  fence  12  ft.  high.  What  did  the  boards  cost  at 
$13  per  M.  ? 

881.  Divide  T8T  of  27|  by  ft  of  22f ,  and  to  the  quotient  add 
-8-2*. 

882.  If  I  buy  40  qts.  of  milk  by  beer  measure,  and  sell  it  by 
wine  measure,  how  many  qts.  do  I  gain  ?  h»?  f  * 

338.  Sold  $4000  in  gold  at  112J,  and  invested  the  proceeds 
in  railroad  stock  at  62,  which  I  sold  soon  after  at  60}.  What 
was  the  amount  of  my  sales,  and  how  much  did  I  gain  ? 

834.  The  circumference  of  a  circle  measures  12  ft.  8  in. 
What  will  72°  45'  of  it  measure  ? 

335.  The  true  discount  of  a  debt  of  $1215  due  in  10  mos. 
and  20  days  is  $90.    What  is  the  rate  ? 

336.  The  solid  contents  of  a  round  log  12  ft.  in  length  are 
171  ft.    What  is  its  diameter  ? 

337.  The  circular  basin  of  a  fountain  is  22£  ft.  in  diameter 
and  2  ft.  8  in.  deep.    How  many  hhds.  of  water  will  it  contain  ? 

338.  If  I  pay  $180.36  for  the  use  of  $3865  for  8  mos.,  what 
would  be  the  principal  on  which  $360.85  is  paid  for  2  yrs.  4 
mos.  15  days  ? 

839.  Find  the  interest  in  U.  S.  money,  at  7T30$,  on  £167 
8s.  3d.  from  June  10, 1871,  to  May  2,  1872. 

340.  At  what  %  will  $1150  in  11  mos.  15  ds.  amount  to 
$1249.18|  ? 

m  Find  value  of  ^f  of  *kgk  +     <£3L. 

342.  What  is  the  difference  in  apothecaries'  weight  between 

7  drams  avoirdupois  weight  and  5  drains  apothecaries'  weight  ? 
843.  What  must  be  the  depth  of  a  cylindrical  cistern  5  ft. 

8  in.  in  diameter,  that  will  contain  25  hhds.  ? 

344.  Sold  a  horse  so  that  J  of  the  gain  equalled  -f5  of  the 
cost.     What  was  the  gain  %  ? 

845.  Bought  a  bill  of  goods  for  $800  ;  and  marked  them  so 
as  to  gain  40$.     After  selling  I  of  them,  A  of  the  remainder 


CHAP.   IV.]  ARITHMETICAL   EXAMPLES.  107 

was  sold  at  25$  discount  from  the  retail  price,  and  the  balance 
was  lost  by  fire.     Did  I  gain  or  lose,  and  what  %  ? 

34.6,  If  a  car-rail  weighs  55  lbs.  to  the  yd.,  what  will  be  the 
weight  of  a  similar  one  §  of  the  same  depth  and  thickness  ? 
347.  What  %  of  the  year  1872  is  the  month  of  May  ? 

8J/8.  A  man  has  3  bins  of  wheat,  containing  700,  950,  and 
1000  bushels  respectively.  He  has  sold  3  lots  of  400  bushels 
each,  1  lot  of  75  bu.  1  pk.  5  qts.,  and  6  lots  each  10  bu.  3  pks. 
2  qts.  What  is  the  value  of  what  he  has  left  at  $1.15  per 
bushel  ? 

SJ/.9.  What  is  the  difference  between  -~-\ — ~— i  of  12 1  x 

of         6 

•J,  and  .65. 

350.  Find  the  cube  root  to  the  third  decimal  place,  of  the 
square  of  327  and  three-fifths. 

851.  What  will  be  the  face  of  a  bill  of  exchange  on  London, 
at  109|,  to  pay  for  11  tons  13  cwt.  3  qrs.  15  lb.  10  oz.  of  sugar 
at  £2  12s.  6d.  per  cwt. ;  and  what  will  be  the  currency  value 
of  the  bill,  gold  being  at  108J  ? 

352.  If  a  baker  sells  a  pound  loaf  for  9  cents  when  flour  is 
worth  $7  per  bbl.>  and  labor  is  $2  per  day;  what  must  he 
charge  for  a  2]  lb.  loaf,  when  flour  is  $4  per  100  lbs.,  and 
labor  is  $1.75  per  day  ? 

358.  What  are  the  dimensions  of  a  yard,  whose  length  is 
twice  its  width,  that  can  be  paved  with  12000  bricks  ? 

354.  How  long  will  it  take  three  two-inch  pipes  to  empty  a 
cistern  which  is  filled  by  two  three-inch  pipes  in  1  hour  and 
20  minutes  ? 

355.  What  is  the  difference  between  the  square  root  of  the 
least  common  multiple  of  6, 12,  18,  36,  48,  and  the  square  of 
the  greatest  common  divisor  of  the  same  numbers  ? 

356.  If  16  yds.  of  cloth  cost  $56,  when  wool  is  75  cts.  per 
To.,  and  labor  is  worth  $2  per  day  of  10  hours,  how  many  yds. 
of  cloth  can  be  purchased  for  $150,  when  wool  is  .60  per  lb., 
and  labor  $1.50  per  day  of  8  hours  ? 

357.  A  laborer  works  18  days,  receiving  for  the  first  day  1 


108  AEITHMETICAL   EXAMPLES.  [CHAP.   IV. 

mill,  2  mills  for  the  second,  4  for  the  third,  and  so  on.    What 
is  the  whole  amount  received  ? 

858.  If  10  men  mow  25  acres  of  grass  in  2  days  of  10  hours 
each,  how  many  hours  per  day  must  6  men  work  to  mow  28 
acres  in  4  days  ? 

359.  Bought  wheat  at  $1.10  per  bushel.  Allowing  that  the 
waste  has  been  If  $,  how  must  I  sell  it  to  gain  8%  ? 

860.  My  agent  in  Havana  has  purchased  for  me  4500  boxes 
of  sugar,  400  lbs.  each,  at  6{  cts.  per  lb.,  and  2150  hhds.  mo- 
lasses at  39£  cts.  per  gal.  When  exchange  is  at  Z\%  premium, 
gold  at  lllg,  and  commission  3\%,  what  will  be  the  currency 
value  of  a  draft  on  Havana  to  pay  all  expenses  ? 

361.  In  a  square  lot  containing  f  of  an  acre,  how  far  is  the 
centre  from  each  corner  and  from  the  centre  of  each  side  ? 

862.  What  is  the  outside  length  of  one  side  of  a  cubical  cis- 
tern 1  brick  in  thickness,  that  will  contain  33  hhds.  ? 

863.  When  gold  is  quoted  at  112|,  what  amount  in  cur- 
rency will  be  necessary,  May  2,  to  pay  a  demand  of  $1500  due 
in  gold  August  17  ? 

86Jf.  How  many  cubic  yards  of  earth  will  be  necessary  to 
cover  T3g  of  an  acre  8  in.  deep  ? 

365.  How  many  acres  of  land  will  be  required  for  an  or- 
chard of  1600  trees  set  in  rows  2  jods  apart  each  way,  there 
being  also  a  space  of  20  ft.  all  round  outside  the  trees  ? 

366.  A  commission  merchant  has  sold  for  me  1500  bales  of 
cotton  cloth,  each  bale  containing  42  pieces,  of  32J  yds.,  at  9| 
cts.  per  yd.,  and  invested  the  proceeds  in  cotton  at  23|  cts. 
per  lb.  If  he  charges  2%  for  selling,  and  \\%  for  purchasing, 
what  number  of  pounds  of  cotton  does  he  send  me  ? 

867.  Bought  5  shares  of  railroad  stock  at  108.J,  and  after 
keeping  it  11  months,  received  a  dividend  of  $7  per  share,  and 
then  sold  the  stock  at  109^.  What  %  did  I  receive  on  my 
investment  ? 

868.  In  what  time  will  money  double  itself  at  \\%  pel 
month  simple  interest  ? 


U^.  i^J 


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